Unit 8. Quadrilaterals. Academic Geometry Spring Name Teacher Period

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Unit 8. Quadrilaterals. Academic Geometry Spring Name Teacher Period"

Transcription

1 Unit 8 Quadrilaterals Academic Geometry Spring 2014 Name Teacher Period

2 1

3 2

4 3

5 Unit 8 at a glance Quadrilaterals This unit focuses on revisiting prior knowledge of polygons and extends to formulate, test, and apply conjectures about quadrilaterals. Students will be able to identify quadrilaterals by the given properties and apply the properties to solve both purely mathematical and real world situations. Essential Questions How are polygons related? What properties do they share? What are the differences and similarities between the types of quadrilaterals (square, rectangle, rhombus, parallelogram, trapezoid, and kite)? And how does knowing this help me? In Unit 8, students will Apply the terms convex, concave, n-gon, equilateral, equiangular, and regular to describe polygons when solving problems involving area, perimeter and circumference in both real-world and purely mathematical situations; Formulate, test, and apply conjectures (based on explorations and concrete models) involving the sum of the measures of interior and exterior angles of convex polygons and the measures of each interior and exterior angle of a regular polygon to solve problems in both real-world and purely mathematical situations; Formulate, test, and apply conjectures (based on explorations and concrete models) involving the properties of parallelogram (including angle and side measure relationships) to solve problems in both real-world and purely mathematical situations; Formulate, test, and apply conjectures (based on explorations and concrete models) involving the conditions that ensure a quadrilateral is a parallelogram including opposite side, opposite angle and diagonal relationships and solve problems in both real-world and purely mathematical situations requiring axiomatic and coordinate approaches; Formulate, test, and apply conjectures (based on explorations and concrete models) involving the properties of rhombuses, rectangles and squares to solve problems in both real-world and purely mathematical situations; 4

6 Formulate, test, and apply conjectures (based on explorations and concrete models) involving the properties of trapezoids and kites to solve problems in both real-world and purely mathematical situations requiring axiomatic or coordinate geometry approaches; Compare and contrast quadrilaterals (parallelograms, rhombuses, rectangles, squares, trapezoids, kites) and their properties to identify them and to solve problems in both real-world and purely mathematical situations. 5

7 Vocabulary concave polygons convex polygons diagonal equiangular exterior angles interior angles isosceles trapezoid kite midsegment n-gons opposite angle parallelogram quadrilateral rectangle regular polygons rhombus square trapezoid vertices 6

8 7

9 Meet the Quadrilateral Family *Parallelogram I have: - 2 sets of parallel sides - 2 sets of congruent sides - opposite angles congruent - consecutive angles supplementary - diagonals bisect each other *Rhombus I have all of the properties of the parallelogram PLUS - 4 congruent sides - diagonals bisect angles - diagonals perpendicular *Rectangle I have all of the properties of the parallelogram PLUS - 4 right angles - diagonals congruent *Square Hey, look at me! I have all of the properties of the parallelogram AND the rectangle AND the rhombus. I have it all! *Quadrilateral I have exactly four sides. 0 *Trapezoid I have only one set of parallel sides. *Isosceles Trapezoid I have: - only one set of parallel sides - base angles congruent - legs congruent - diagonals congruent - opposite angles supplementary *Kite I have: - 2 sets of consecutive congruent sides - only one pair of opposite angles congruent - diagonals perpendicular 8

10 9

11 8.1 NOTES Essential Vocabulary Polygon Not Polygons Concave Convex Equilateral Equiangular Regular Triangle Octagon Quadrilateral Nonagon Pentagon Decagon Hexagon Dodecagon Heptagon n-gon (an n-sided shape) ANY shape can be called n -gon based on the number of sides. Polygons with more than 10 sides are usually referred to as n -gons Ex. 14-gon, 32-gon, 100-gon 10

12 Interior and Exterior Angles of a Polygon In a polygon, two vertices that are endpoints of the same side are called consecutive vertices. A diagonal of a polygon joins two non-consecutive vertices of a polygon. Consecutive vertices Choose any vertex and draw every diagonal possible from that vertex. Notice that when you draw all the diagonals of a polygon from one vertex, you divide the polygon into. Recall that the triangle sum theorem states. For each polygon in the table, draw all the diagonals from one vertex. Complete the table. Polygon # of Sides # of triangles formed Interior Angle Sum of Polygon Triangle Quadrilateral Pentagon Hexagon Heptagon n-gon POLYGON INTERIOR ANGLES THEOREM: For an n-sided convex polygon, the sum of all the interior angles is. 11

13 The exterior angle sum of a polygon does not depend on the number of sides on the polygon. To prove this, use the diagrams below to calculate each exterior angle of the polygons. Remember that an interior angle and its adjacent exterior angle form a linear pair (so their sum is ). triangle quadrilateral pentagon 50⁰ 85⁰ 110⁰ 130⁰ 125⁰ 115⁰ 85⁰ 55⁰ 90⁰ 40⁰ 95⁰ 100⁰ Interior angle sum 180⁰ 360⁰ 540⁰ Exterior angle sum POLYGON EXTERIOR ANGLES THEOREM: The sum of all the exterior angles of a convex polygon (one exterior angle at each vertex is always. Example 1: Find the sum of the measures of the interior angles of a convex octagon. Example 2: The sum of the measures of the interior angles of a convex polygon is 1440⁰. How many sides does the polygon have? 12

14 Example 3: Find the value of x. Example 4: A trampoline is shaped like a regular dodecagon (12 sides). Find the measure of each interior and exterior angle. Example 5: Find the value of x. 13

15 8.1 HOMEWORK Find the sum of the measures of the interior angles of the indicated convex polygon gon gon The sum of the measures of the interior angles of a convex polygon is given. Classify the polygon by the number of sides Find the value of

16 8. The measures of the interior angles of a convex octagon are and What is the measure of the smallest interior angle? Find the measures of an interior angle and an exterior angle of the indicated polygon. 9. Regular Octagon 10. Regular 100-gon 11. The side view of a storage shed is shown below. Find the value of. Then determine the measure of each angle. 15

17 8.2 NOTES Properties of Parallelograms DEFINITION: A parallelogram is a quadrilateral with. You can call this figure: Parallelogram PQRS or. In, and, by definition. Other properties: If a quadrilateral is a parallelogram, then. THM 8.3 THM 8.4 THM 8.5 THM 8.6 Ex1: Find the values of x and y. Your thoughts: 1) Is it a parallelogram? YES, b/c the opp. sides are parallel (def.) 2) Opposite sides are congruent, so x + 4 = 12. 3) Opposite angles are congruent, so y = 65. Ex 2: 16

18 Ex 3-6: Ex 7: The measure of one interior angle of a parallelogram is 50 degrees more than 4 times the measure of another angle. Find the measure of each angle. (Make a sketch and label it.) Ex 8: In LMNO, the ratio of LM to MN is 4:3. Find LM if the perimeter of LMNO is 28. Ex 9: The diagonals of LMNO intersect at point P. What are the coordinates of P? Hint: What do you need to know? 17

19 Ex 10: Is the quadrilateral formed by the lines on the graph a parallelogram? Hint: What do you need to know? 18

20 19

21 8.2 HOMEWORK Find the measure of the indicated angle in the parallelogram. 1. Find 2. Find Find the value of each variable in parallelogram Find the indicated measure in

22 Use the diagram of Points and are midpoints of and Find the indicated measure In parallelogram the ratio of to is. Find if the perimeter of is. 21

23 8.3 NOTES Proving a Quadrilateral is a Parallelogram Examples: 22

24 23

25 8.3 HOMEWORK What theorem can you use to show that the quadrilateral is a parallelogram? For what value of is the quadrilateral a parallelogram?

26 The vertices of quadrilateral are given. Draw in a coordinate plane and show that it is a parallelogram. 11. ( ) ( ) ( ) ( ) 12. ( ) ( ) ( ) ( ) 25

27 8.4NOTES Rhombuses, Squares and Rectangles In this lesson, you will learn about three special types of parallelograms: Rhombus Rectangle Square A parallelogram with four right angles (equiangular). A parallelogram with four congruent sides (equilateral). SPECIAL NOTES ABOUT SQUARES: A parallelogram with four congruent sides and four right angles (regular). Since a square has four congruent sides, it is also a. Since a square has four right angles, it is also a. Diagonals of Rhombuses and Rectangles 26

28 Examples: Name each quadrilateral parallelogram, rectangle, rhombus, and square for which the statement is true. 1. It is equiangular. 2. It is equiangular and equilateral. 3. It is diagonals are perpendicular. 4. Opposite sides are congruent. 5. The diagonals bisect each other. 6. The diagonals bisect opposite angles. Classify the special quadrilateral. Explain your reasoning. Then find the values of and In the rhombus to the right, given. Find all the other angles. 27

29 10. Given rectangle CERT and, find each measure. 11. Given rectangle CERT, (1) If and, solve for. (2) If and, solve for. 28

30 29

31 30

32 31

33 8.4 HOMEWORK For any rhombus decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning For any rectangle decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning Classify the quadrilateral. Explain your reasoning

34 Classify the special quadrilateral. Explain your reasoning. Then find the values of and The diagonals of rhombus intersect at Given that and find the indicated measure In preparation for a storm, a window is protected by nailing boards along its diagonals. The lengths of the boards are the same. Can you conclude that the window is a square? Explain. 33

35 8.5/8.6 NOTES Trapezoids & Kites DEFINITION: A trapezoid is a quadrilateral with. The parallel sides are called the. The non-parallel sides are called the. Since a trapezoid has two bases, it has two pairs of. DEFINITION: An isosceles trapezoid is one in which the. Think of it as an isosceles triangle with the top cut off by a segment parallel to a base. *An isosceles trapezoid has: (THM 8.14) (THM 8.16) 34

36 DEFINITION: The midsegment of a trapezoid is a segment that connects the of its. (THM 8.17) The midsegment of a trapezoid is parallel to each base and measures on half the sum of the base lengths. If MN is the midsegment of trapezoid ABCD, 1 then MN AB, MN DC, and MN (AB CD) 2 **In other words, Examples: 1. Find and. 2. Find the length of the midsegment. 3. Solve for. 4. In trapezoid, and. The midsegment is. Sketch and its midsegment and find. 35

37 DEFINITION: A kite is a quadrilateral with. THREE RULES FOR KITES 36

38 37

39 UNIT 8 PERFORMANCE TASK Performance of a Lifetime You are a dance choreographer and have been asked by the Houston Rockets to come up with a 45 second dance that will be showcased during a playoff game. You have been allowed to use the entire court for the performance and have been asked to make sure that all sides of the viewing audience will be able to see the performance without using the Jumbotron. Your goal is to fill the 94 x 50 foot court by placing the dancers in the shape of a polygon. You want to make sure that you use as much of the court as possible while making sure that there is an equal amount of unused space at each corner of the court. 1. Determine where the vertices of your polygon must fall to develop an equal amount of unused space so all fans can see the performance and the owner of the Houston Rockets will be happy. How would you find these points and how do you know the unused space is equal at each corner of the court? 2. What type of polygon is created? How can you justify your answer? Justify all of the polygon s properties. 38

40 39

Geometry. Unit 6. Quadrilaterals. Unit 6

Geometry. Unit 6. Quadrilaterals. Unit 6 Geometry Quadrilaterals Properties of Polygons Formed by three or more consecutive segments. The segments form the sides of the polygon. Each side intersects two other sides at its endpoints. The intersections

More information

Unit 3: Triangle Bisectors and Quadrilaterals

Unit 3: Triangle Bisectors and Quadrilaterals Unit 3: Triangle Bisectors and Quadrilaterals Unit Objectives Identify triangle bisectors Compare measurements of a triangle Utilize the triangle inequality theorem Classify Polygons Apply the properties

More information

8.1 Find Angle Measures in Polygons

8.1 Find Angle Measures in Polygons 8.1 Find Angle Measures in Polygons Obj.: To find angle measures in polygons. Key Vocabulary Diagonal - A diagonal of a polygon is a segment that joins two nonconsecutive vertices. Polygon ABCDE has two

More information

Sum of the interior angles of a n-sided Polygon = (n-2) 180

Sum of the interior angles of a n-sided Polygon = (n-2) 180 5.1 Interior angles of a polygon Sides 3 4 5 6 n Number of Triangles 1 Sum of interiorangles 180 Sum of the interior angles of a n-sided Polygon = (n-2) 180 What you need to know: How to use the formula

More information

6-1 Properties and Attributes of Polygons

6-1 Properties and Attributes of Polygons 6-1 Properties and Attributes of Polygons Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up 1. A? is a three-sided polygon. triangle 2. A? is a four-sided polygon. quadrilateral Evaluate each expression

More information

Polygons are figures created from segments that do not intersect at any points other than their endpoints.

Polygons are figures created from segments that do not intersect at any points other than their endpoints. Unit #5 Lesson #1: Polygons and Their Angles. Polygons are figures created from segments that do not intersect at any points other than their endpoints. A polygon is convex if all of the interior angles

More information

11.3 Curves, Polygons and Symmetry

11.3 Curves, Polygons and Symmetry 11.3 Curves, Polygons and Symmetry Polygons Simple Definition A shape is simple if it doesn t cross itself, except maybe at the endpoints. Closed Definition A shape is closed if the endpoints meet. Polygon

More information

Honors Packet on. Polygons, Quadrilaterals, and Special Parallelograms

Honors Packet on. Polygons, Quadrilaterals, and Special Parallelograms Honors Packet on Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 6-1) SWBAT: Find measures of interior and exterior angles of polygons Pgs: #1 6 in packet HW: Pages 386

More information

CHAPTER 6. Polygons, Quadrilaterals, and Special Parallelograms

CHAPTER 6. Polygons, Quadrilaterals, and Special Parallelograms CHAPTER 6 Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 6-1) SWBAT: Find measures of interior and exterior angles of polygons Pgs: 1-7 HW: Pgs: 8-10 DAY 2: (6-2) Pgs:

More information

TEKS: G2B, G3B, G4A, G5A, G5B, G9B The student will determine the validity of conjectures. The student will construct and justify statements.

TEKS: G2B, G3B, G4A, G5A, G5B, G9B The student will determine the validity of conjectures. The student will construct and justify statements. TEKS: G2B, G3B, G4A, G5A, G5B, G9B The student will determine the validity of conjectures. The student will construct and justify statements. The student will select an appropriate representation to solve

More information

7.3 & 7.4 Polygon Formulas completed.notebook January 10, 2014

7.3 & 7.4 Polygon Formulas completed.notebook January 10, 2014 Chapter 7 Polygons Polygon 1. Closed Figure # of Sides Polygon Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 2. Straight sides/edges 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon 15 Pentadecagon

More information

Unit 8. Ch. 8. "More than three Sides"

Unit 8. Ch. 8. More than three Sides Unit 8. Ch. 8. "More than three Sides" 1. Use a straightedge to draw CONVEX polygons with 4, 5, 6 and 7 sides. 2. In each draw all of the diagonals from ONLY ONE VERTEX. A diagonal is a segment that joins

More information

Target To know the properties of a rectangle

Target To know the properties of a rectangle Target To know the properties of a rectangle (1) A rectangle is a 3-D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles

More information

Chapter Three. Parallel Lines and Planes

Chapter Three. Parallel Lines and Planes Chapter Three Parallel Lines and Planes Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately

More information

(n = # of sides) One interior angle:

(n = # of sides) One interior angle: 6.1 What is a Polygon? Regular Polygon- Polygon Formulas: (n = # of sides) One interior angle: 180(n 2) n Sum of the interior angles of a polygon = 180 (n - 2) Sum of the exterior angles of a polygon =

More information

Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid

Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid Quadrilaterals Properties of a parallelogram, a rectangle, a rhombus, a square, and a trapezoid Grade level: 10 Prerequisite knowledge: Students have studied triangle congruences, perpendicular lines,

More information

Topics Covered on Geometry Placement Exam

Topics Covered on Geometry Placement Exam Topics Covered on Geometry Placement Exam - Use segments and congruence - Use midpoint and distance formulas - Measure and classify angles - Describe angle pair relationships - Use parallel lines and transversals

More information

1. An isosceles trapezoid does not have perpendicular diagonals, and a rectangle and a rhombus are both parallelograms.

1. An isosceles trapezoid does not have perpendicular diagonals, and a rectangle and a rhombus are both parallelograms. Quadrilaterals - Answers 1. A 2. C 3. A 4. C 5. C 6. B 7. B 8. B 9. B 10. C 11. D 12. B 13. A 14. C 15. D Quadrilaterals - Explanations 1. An isosceles trapezoid does not have perpendicular diagonals,

More information

Geometry. 1.4 Perimeter and Area in the Coordinate Plane

Geometry. 1.4 Perimeter and Area in the Coordinate Plane Geometry 1.4 Perimeter and Area in the Coordinate Plane Essential Question How can I find the perimeter and area of a polygon in a coordinate plane? What You Will Learn Classify polygons Find perimeters

More information

Geometry 8-1 Angles of Polygons

Geometry 8-1 Angles of Polygons . Sum of Measures of Interior ngles Geometry 8-1 ngles of Polygons 1. Interior angles - The sum of the measures of the angles of each polygon can be found by adding the measures of the angles of a triangle.

More information

POLYGONS

POLYGONS POLYGONS 8.1.1 8.1.5 After studying triangles and quadrilaterals, students now extend their study to all polygons. A polygon is a closed, two-dimensional figure made of three or more nonintersecting straight

More information

November 11, Polygons. poly means "many" gon means "angles" polygon means "many angles"

November 11, Polygons. poly means many gon means angles polygon means many angles 3.5 Polygons poly means "many" gon means "angles" polygon means "many angles" note that each polygon is formed by coplanar segments (called sides) such that: each segment intersects exactly 2 other segments,

More information

A convex polygon is a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon.

A convex polygon is a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon. hapter 7 Polygons A polygon can be described by two conditions: 1. No two segments with a common endpoint are collinear. 2. Each segment intersects exactly two other segments, but only on the endpoints.

More information

6-1 Angles of Polygons

6-1 Angles of Polygons Find the sum of the measures of the interior angles of each convex polygon. 1. decagon A decagon has ten sides. Use the Polygon Interior Angles Sum Theorem to find the sum of its interior angle measures.

More information

Objectives. Cabri Jr. Tools

Objectives. Cabri Jr. Tools Activity 24 Angle Bisectors and Medians of Quadrilaterals Objectives To investigate the properties of quadrilaterals formed by angle bisectors of a given quadrilateral To investigate the properties of

More information

15 Polygons. 15.1 Angle Facts. Example 1. Solution. Example 2. Solution

15 Polygons. 15.1 Angle Facts. Example 1. Solution. Example 2. Solution 15 Polygons MEP Y8 Practice Book B 15.1 Angle Facts In this section we revise some asic work with angles, and egin y using the three rules listed elow: The angles at a point add up to 360, e.g. a c a +

More information

56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.

56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points. 6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S2495808) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which

More information

Name: 22K 14A 12T /48 MPM1D Unit 7 Review True/False (4K) Indicate whether the statement is true or false. Show your work

Name: 22K 14A 12T /48 MPM1D Unit 7 Review True/False (4K) Indicate whether the statement is true or false. Show your work Name: _ 22K 14A 12T /48 MPM1D Unit 7 Review True/False (4K) Indicate whether the statement is true or false. Show your work 1. An equilateral triangle always has three 60 interior angles. 2. A line segment

More information

Quadrilaterals GETTING READY FOR INSTRUCTION

Quadrilaterals GETTING READY FOR INSTRUCTION Quadrilaterals / Mathematics Unit: 11 Lesson: 01 Duration: 7 days Lesson Synopsis: In this lesson students explore properties of quadrilaterals in a variety of ways including concrete modeling, patty paper

More information

The angle sum property of triangles can help determine the sum of the measures of interior angles of other polygons.

The angle sum property of triangles can help determine the sum of the measures of interior angles of other polygons. Interior Angles of Polygons The angle sum property of triangles can help determine the sum of the measures of interior angles of other polygons. The sum of the measures of the interior angles of a triangle

More information

The Polygon Angle-Sum Theorems

The Polygon Angle-Sum Theorems 6-1 The Polygon Angle-Sum Theorems Common Core State Standards G-SRT.B.5 Use congruence... criteria to solve problems and prove relationships in geometric figures. MP 1, MP 3 Objectives To find the sum

More information

UNIT H1 Angles and Symmetry Activities

UNIT H1 Angles and Symmetry Activities UNIT H1 Angles and Symmetry Activities Activities H1.1 Lines of Symmetry H1.2 Rotational and Line Symmetry H1.3 Symmetry of Regular Polygons H1.4 Interior Angles in Polygons Notes and Solutions (1 page)

More information

1 of 69 Boardworks Ltd 2004

1 of 69 Boardworks Ltd 2004 1 of 69 2 of 69 Intersecting lines 3 of 69 Vertically opposite angles When two lines intersect, two pairs of vertically opposite angles are formed. a d b c a = c and b = d Vertically opposite angles are

More information

Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.

Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry. Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know

More information

Unit 8 Geometry QUADRILATERALS. NAME Period

Unit 8 Geometry QUADRILATERALS. NAME Period Unit 8 Geometry QUADRILATERALS NAME Period 1 A little background Polygon is the generic term for a closed figure with any number of sides. Depending on the number, the first part of the word Poly is replaced

More information

parallel lines perpendicular lines intersecting lines vertices lines that stay same distance from each other forever and never intersect

parallel lines perpendicular lines intersecting lines vertices lines that stay same distance from each other forever and never intersect parallel lines lines that stay same distance from each other forever and never intersect perpendicular lines lines that cross at a point and form 90 angles intersecting lines vertices lines that cross

More information

Geometry Concepts. Figures that lie in a plane are called plane figures. These are all plane figures. Triangle 3

Geometry Concepts. Figures that lie in a plane are called plane figures. These are all plane figures. Triangle 3 Geometry Concepts Figures that lie in a plane are called plane figures. These are all plane figures. Polygon No. of Sides Drawing Triangle 3 A polygon is a plane closed figure determined by three or more

More information

Algebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids

Algebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids Algebra III Lesson 33 Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids Quadrilaterals What is a quadrilateral? Quad means? 4 Lateral means?

More information

A Different Look at Trapezoid Area Prerequisite Knowledge

A Different Look at Trapezoid Area Prerequisite Knowledge Prerequisite Knowledge Conditional statement an if-then statement (If A, then B) Converse the two parts of the conditional statement are reversed (If B, then A) Parallel lines are lines in the same plane

More information

Page How many sides does an octagon have? a) 4 b) 5 c) 6 d) 8 e) A regular hexagon has lines of symmetry. a) 2 b) 3 c) 4 d) 5 e) 6 1 9

Page How many sides does an octagon have? a) 4 b) 5 c) 6 d) 8 e) A regular hexagon has lines of symmetry. a) 2 b) 3 c) 4 d) 5 e) 6 1 9 Acc. Geometery Name Polygon Review Per/Sec. Date Determine whether each of the following statements is always, sometimes, or never true. 1. A regular polygon is convex. 2. Two sides of a polygon are noncollinear.

More information

10.1: Areas of Parallelograms and Triangles

10.1: Areas of Parallelograms and Triangles 10.1: Areas of Parallelograms and Triangles Important Vocabulary: By the end of this lesson, you should be able to define these terms: Base of a Parallelogram, Altitude of a Parallelogram, Height of a

More information

Conjectures. Chapter 2. Chapter 3

Conjectures. Chapter 2. Chapter 3 Conjectures Chapter 2 C-1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C-2 Vertical Angles Conjecture If two angles are vertical

More information

39 Symmetry of Plane Figures

39 Symmetry of Plane Figures 39 Symmetry of Plane Figures In this section, we are interested in the symmetric properties of plane figures. By a symmetry of a plane figure we mean a motion of the plane that moves the figure so that

More information

Conjectures for Geometry for Math 70 By I. L. Tse

Conjectures for Geometry for Math 70 By I. L. Tse Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:

More information

Chapter 1: Essentials of Geometry

Chapter 1: Essentials of Geometry Section Section Title 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence 1.3 Use Midpoint and Distance Formulas Chapter 1: Essentials of Geometry Learning Targets I Can 1. Identify,

More information

LEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable.

LEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable. Name LEVEL G, SKILL 1 Class Be sure to show all work.. Leave answers in terms of ϖ where applicable. 1. What is the area of a triangle with a base of 4 cm and a height of 6 cm? 2. What is the sum of the

More information

INFORMATION FOR TEACHERS

INFORMATION FOR TEACHERS INFORMATION FOR TEACHERS The math behind DragonBox Elements - explore the elements of geometry - Includes exercises and topics for discussion General information DragonBox Elements Teaches geometry through

More information

Lesson 28: Properties of Parallelograms

Lesson 28: Properties of Parallelograms Student Outcomes Students complete proofs that incorporate properties of parallelograms. Lesson Notes Throughout this module, we have seen the theme of building new facts with the use of established ones.

More information

Line. A straight path that continues forever in both directions.

Line. A straight path that continues forever in both directions. Geometry Vocabulary Line A straight path that continues forever in both directions. Endpoint A point that STOPS a line from continuing forever, it is a point at the end of a line segment or ray. Ray A

More information

Analysis in Geometry. By Danielle Long. Grade Level: 8 th. Time: 5-50 minute periods. Technology used: Geometer s sketchpad Geoboards NLVM website

Analysis in Geometry. By Danielle Long. Grade Level: 8 th. Time: 5-50 minute periods. Technology used: Geometer s sketchpad Geoboards NLVM website Analysis in Geometry By Danielle Long Grade Level: 8 th Time: 5-50 minute periods Technology used: Geometer s sketchpad Geoboards NLVM website 1 NCTM Standards Addressed Problem Solving Geometry Algebra

More information

1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area?

1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area? 1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area? (a) 20 ft x 19 ft (b) 21 ft x 18 ft (c) 22 ft x 17 ft 2. Which conditional

More information

Quadrilaterals Unit Review

Quadrilaterals Unit Review Name: Class: Date: Quadrilaterals Unit Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. ( points) In which polygon does the sum of the measures of

More information

22.1 Interior and Exterior Angles

22.1 Interior and Exterior Angles Name Class Date 22.1 Interior and Exterior ngles Essential Question: What can you say about the interior and exterior angles of a triangle and other polygons? Resource Locker Explore 1 Exploring Interior

More information

Definitions, Postulates and Theorems

Definitions, Postulates and Theorems Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven

More information

Properties of Special Parallelograms

Properties of Special Parallelograms Properties of Special Parallelograms Lab Summary: This lab consists of four activities that lead students through the construction of a parallelogram, a rectangle, a square, and a rhombus. Students then

More information

Date: Period: Symmetry

Date: Period: Symmetry Name: Date: Period: Symmetry 1) Line Symmetry: A line of symmetry not only cuts a figure in, it creates a mirror image. In order to determine if a figure has line symmetry, a figure can be divided into

More information

Centroid: The point of intersection of the three medians of a triangle. Centroid

Centroid: The point of intersection of the three medians of a triangle. Centroid Vocabulary Words Acute Triangles: A triangle with all acute angles. Examples 80 50 50 Angle: A figure formed by two noncollinear rays that have a common endpoint and are not opposite rays. Angle Bisector:

More information

GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT!

GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT! GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT! FINDING THE DISTANCE BETWEEN TWO POINTS DISTANCE FORMULA- (x₂-x₁)²+(y₂-y₁)² Find the distance between the points ( -3,2) and

More information

PROPERTIES OF TRIANGLES AND QUADRILATERALS

PROPERTIES OF TRIANGLES AND QUADRILATERALS Mathematics Revision Guides Properties of Triangles, Quadrilaterals and Polygons Page 1 of 21 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier PROPERTIES OF TRIANGLES AND QUADRILATERALS

More information

Five-Minute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts:

Five-Minute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts: Five-Minute Check (over Lesson 1 5) CCSS Then/Now New Vocabulary Key Concepts: Polygons Example 1: Name and Classify Polygons Key Concepts: Perimeter, Circumference, and Area Example 2: Find Perimeter

More information

Geometry Module 4 Unit 2 Practice Exam

Geometry Module 4 Unit 2 Practice Exam Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning

More information

Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade

Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade Standards/Content Padrões / Conteúdo Learning Objectives Objetivos de Aprendizado Vocabulary Vocabulário Assessments Avaliações Resources

More information

BASIC GEOMETRY GLOSSARY

BASIC GEOMETRY GLOSSARY BASIC GEOMETRY GLOSSARY Acute angle An angle that measures between 0 and 90. Examples: Acute triangle A triangle in which each angle is an acute angle. Adjacent angles Two angles next to each other that

More information

CONJECTURES - Discovering Geometry. Chapter 2

CONJECTURES - Discovering Geometry. Chapter 2 CONJECTURES - Discovering Geometry Chapter C-1 Linear Pair Conjecture - If two angles form a linear pair, then the measures of the angles add up to 180. C- Vertical Angles Conjecture - If two angles are

More information

A of a polygon is a segment that joins two nonconsecutive vertices. 1. How many degrees are in a triangle?

A of a polygon is a segment that joins two nonconsecutive vertices. 1. How many degrees are in a triangle? 8.1- Find Angle Measures in Polygons SWBAT: find interior and exterior angle measures in polygons. Common Core: G.CO.11, G.CO.13, G.SRT.5 Do Now Fill in the blank. A of a polygon is a segment that joins

More information

INDEX. Arc Addition Postulate,

INDEX. Arc Addition Postulate, # 30-60 right triangle, 441-442, 684 A Absolute value, 59 Acute angle, 77, 669 Acute triangle, 178 Addition Property of Equality, 86 Addition Property of Inequality, 258 Adjacent angle, 109, 669 Adjacent

More information

6-5 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure.

6-5 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 1. If, find. A rhombus is a parallelogram with all four sides congruent. So, Then, is an isosceles triangle. Therefore, If a parallelogram

More information

**The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle.

**The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle. Geometry Week 7 Sec 4.2 to 4.5 section 4.2 **The Ruler Postulate guarantees that you can measure any segment. **The Protractor Postulate guarantees that you can measure any angle. Protractor Postulate:

More information

Situation: Proving Quadrilaterals in the Coordinate Plane

Situation: Proving Quadrilaterals in the Coordinate Plane Situation: Proving Quadrilaterals in the Coordinate Plane 1 Prepared at the University of Georgia EMAT 6500 Date Last Revised: 07/31/013 Michael Ferra Prompt A teacher in a high school Coordinate Algebra

More information

Geo - CH6 Practice Test

Geo - CH6 Practice Test Geo - H6 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the measure of each exterior angle of a regular decagon. a. 45 c. 18 b. 22.5

More information

Intermediate Math Circles October 10, 2012 Geometry I: Angles

Intermediate Math Circles October 10, 2012 Geometry I: Angles Intermediate Math Circles October 10, 2012 Geometry I: Angles Over the next four weeks, we will look at several geometry topics. Some of the topics may be familiar to you while others, for most of you,

More information

1.1. Building Blocks of Geometry EXAMPLE. Solution a. P is the midpoint of both AB and CD. Q is the midpoint of GH. CONDENSED

1.1. Building Blocks of Geometry EXAMPLE. Solution a. P is the midpoint of both AB and CD. Q is the midpoint of GH. CONDENSED CONDENSED LESSON 1.1 Building Blocks of Geometry In this lesson you will Learn about points, lines, and planes and how to represent them Learn definitions of collinear, coplanar, line segment, congruent

More information

Angles that are between parallel lines, but on opposite sides of a transversal.

Angles that are between parallel lines, but on opposite sides of a transversal. GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,

More information

6-5 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure.

6-5 Rhombi and Squares. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. ALGEBRA Quadrilateral ABCD is a rhombus. Find each value or measure. 3. PROOF Write a two-column proof to prove that if ABCD is a rhombus with diagonal. 1. If, find. A rhombus is a parallelogram with all

More information

Upper Elementary Geometry

Upper Elementary Geometry Upper Elementary Geometry Geometry Task Cards Answer Key The unlicensed photocopying, reproduction, display, or projection of the material, contained or accompanying this publication, is expressly prohibited

More information

Geometry Vocabulary Booklet

Geometry Vocabulary Booklet Geometry Vocabulary Booklet Geometry Vocabulary Word Everyday Expression Example Acute An angle less than 90 degrees. Adjacent Lying next to each other. Array Numbers, letter or shapes arranged in a rectangular

More information

M 1312 Section Trapezoids

M 1312 Section Trapezoids M 1312 Section 4.4 1 Trapezoids Definition: trapezoid is a quadrilateral with exactly two parallel sides. Parts of a trapezoid: Base Leg Leg Leg Base Base Base Leg Isosceles Trapezoid: Every trapezoid

More information

SHAPE, SPACE AND MEASURES

SHAPE, SPACE AND MEASURES SHAPE, SPACE AND MEASURES Pupils should be taught to: Use accurately the vocabulary, notation and labelling conventions for lines, angles and shapes; distinguish between conventions, facts, definitions

More information

Estimating Angle Measures

Estimating Angle Measures 1 Estimating Angle Measures Compare and estimate angle measures. You will need a protractor. 1. Estimate the size of each angle. a) c) You can estimate the size of an angle by comparing it to an angle

More information

Sum of the interior angles of a (n - 2)180 polygon ~, Sum of the exterior angles of a 360 polygon

Sum of the interior angles of a (n - 2)180 polygon ~, Sum of the exterior angles of a 360 polygon Name Geometry Polygons Sum of the interior angles of a (n - 2)180 polygon ~, Sum of the exterior angles of a 360 polygon Each interior angle of a regular (n - 2)180 i polygon n Each exterior angle of a

More information

10-4 Inscribed Angles. Find each measure. 1.

10-4 Inscribed Angles. Find each measure. 1. Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semi-circle. So, intercepted arc. So, 66 4. SCIENCE The diagram shows how light bends in a raindrop to make the colors of the rainbow. If, what

More information

Geometry Course Summary Department: Math. Semester 1

Geometry Course Summary Department: Math. Semester 1 Geometry Course Summary Department: Math Semester 1 Learning Objective #1 Geometry Basics Targets to Meet Learning Objective #1 Use inductive reasoning to make conclusions about mathematical patterns Give

More information

MATH 139 FINAL EXAM REVIEW PROBLEMS

MATH 139 FINAL EXAM REVIEW PROBLEMS MTH 139 FINL EXM REVIEW PROLEMS ring a protractor, compass and ruler. Note: This is NOT a practice exam. It is a collection of problems to help you review some of the material for the exam and to practice

More information

Math 6: Unit 7: Geometry Notes 2-Dimensional Figures

Math 6: Unit 7: Geometry Notes 2-Dimensional Figures Math 6: Unit 7: Geometry Notes -Dimensional Figures Prep for 6.G.A.1 Classifying Polygons A polygon is defined as a closed geometric figure formed by connecting line segments endpoint to endpoint. Polygons

More information

(a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units

(a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units 1. Find the area of parallelogram ACD shown below if the measures of segments A, C, and DE are 6 units, 2 units, and 1 unit respectively and AED is a right angle. (a) 5 square units (b) 12 square units

More information

Chapters 4 and 5 Notes: Quadrilaterals and Similar Triangles

Chapters 4 and 5 Notes: Quadrilaterals and Similar Triangles Chapters 4 and 5 Notes: Quadrilaterals and Similar Triangles IMPORTANT TERMS AND DEFINITIONS parallelogram rectangle square rhombus A quadrilateral is a polygon that has four sides. A parallelogram is

More information

UNDERSTANDING QUADRILATERALS

UNDERSTANDING QUADRILATERALS UNIT 5 UNDERSTANDING QUADRILATERALS AND PRACTICAL GEOMETRY (A) Main Concepts and Results A simple closed curve made up of only line segments is called a polygon. A diagonal of a polygon is a line segment

More information

Geometry Progress Ladder

Geometry Progress Ladder Geometry Progress Ladder Maths Makes Sense Foundation End-of-year objectives page 2 Maths Makes Sense 1 2 End-of-block objectives page 3 Maths Makes Sense 3 4 End-of-block objectives page 4 Maths Makes

More information

Year 10 Term 1 Homework

Year 10 Term 1 Homework Yimin Math Centre Year 10 Term 1 Homework Student Name: Grade: Date: Score: Table of contents 10 Year 10 Term 1 Week 10 Homework 1 10.1 Deductive geometry.................................... 1 10.1.1 Basic

More information

PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.

PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the

More information

ABC is the triangle with vertices at points A, B and C

ABC is the triangle with vertices at points A, B and C Euclidean Geometry Review This is a brief review of Plane Euclidean Geometry - symbols, definitions, and theorems. Part I: The following are symbols commonly used in geometry: AB is the segment from the

More information

Geometry Honors: Extending 2 Dimensions into 3 Dimensions. Unit Overview. Student Focus. Semester 2, Unit 5: Activity 30. Resources: Online Resources:

Geometry Honors: Extending 2 Dimensions into 3 Dimensions. Unit Overview. Student Focus. Semester 2, Unit 5: Activity 30. Resources: Online Resources: Geometry Honors: Extending 2 Dimensions into 3 Dimensions Semester 2, Unit 5: Activity 30 Resources: SpringBoard- Geometry Online Resources: Geometry Springboard Text Unit Overview In this unit students

More information

Geometric Concepts. Academic Vocabulary composite

Geometric Concepts. Academic Vocabulary composite Geometric Concepts 5 Unit Overview In this unit you will extend your study of polygons as you investigate properties of triangles and quadrilaterals. You will study area, surface area, and volume of two-

More information

/27 Intro to Geometry Review

/27 Intro to Geometry Review /27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the

More information

11-5 Polygons ANSWER: ANSWER: ANSWER:

11-5 Polygons ANSWER: ANSWER: ANSWER: Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why. 1. 5. KALEIDOSCOPE The kaleidoscope image shown is a regular polygon with 14 sides. What

More information

Final Review Problems Geometry AC Name

Final Review Problems Geometry AC Name Final Review Problems Geometry Name SI GEOMETRY N TRINGLES 1. The measure of the angles of a triangle are x, 2x+6 and 3x-6. Find the measure of the angles. State the theorem(s) that support your equation.

More information

3 rd Six Weeks

3 rd Six Weeks Geometry 3 rd Six Weeks 014-015 MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY Nov 9 10 11 1 13 6-1 Angle Measures in Polygons Class: Wksht #1 6- Properties of Parallelograms Class: Wksht # 6-3 Proving Parallelograms

More information

Chapter 1 Basics of Geometry Geometry. For questions 1-5, draw and label an image to fit the descriptions.

Chapter 1 Basics of Geometry Geometry. For questions 1-5, draw and label an image to fit the descriptions. Chapter 1 Basics of Geometry Geometry Name For questions 1-5, draw and label an image to fit the descriptions. 1. intersecting and Plane P containing but not. 2. Three collinear points A, B, and C such

More information

Geometry of 2D Shapes

Geometry of 2D Shapes Name: Geometry of 2D Shapes Answer these questions in your class workbook: 1. Give the definitions of each of the following shapes and draw an example of each one: a) equilateral triangle b) isosceles

More information

Chapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle.

Chapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle. Chapter 3.1 Angles Define what an angle is. Define the parts of an angle. Recall our definition for a ray. A ray is a line segment with a definite starting point and extends into infinity in only one direction.

More information