# (n = # of sides) One interior angle:

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 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 = 360 Polygon Names Sides N Name One exterior angle: 360 n Ex: R O U Name the vertices: Name the sides: Name the diagonals containing G: Name 2 consecutive s: Name 2 nonconsecutive sides: G ngles of Polygons 1

2 1. Find the sum of the measures of the angles of a convex polygon with 14 sides. 2. For the given regular polygon, find the measure of each of its interior angles: a) dodecagon b) 16 gon 3. Find the degree measure of each exterior angle of a regular polygon with 20 sides. 4. For the following measures of an angle of a regular polygon, find the number of sides. a) 160 b) The sum of the interior angles of a convex polygon is Find the number of sides. 6. Find the number of sides of a regular polygon if the measure of one of its interior angles Is three times the measure of its adjacent exterior angle. Show all work. Find the sum of the measures of the angles of a convex polygon with the given # of sides For each of the following, the measure of one angle of a regular convex polygon is given. Find the # of sides For each of the following, the number of sides of a regular polygon is given. Find the measure of each angle Find the degree measure of one exterior angle for a regular polygon with the given # of sides The sum of the measure of the interior angles of a convex polygon is lassify the polygon. 16. The measure of one exterior angle of a regular polygon is 45. lassify the polygon. 17. Find the number of sides of a regular polygon, if the measure of one of its interior angles equals the measure of its adjacent exterior angle. 18. Find the number of sides of a regular polygon, if the measure of one of its interior angles equals twice the measure of the adjacent exterior angle. 19. lassify the regular polygon, if the measure of one of its interior angles equals one-half the measure of the adjacent exterior angle. 20. If the sum of the measures of six interior angles of a heptagon is 755, what is the measure of the remaining angle? Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides For a polygon to be regular, it must be both equiangular and equilateral. Name the only type of polygon that must be regular if it is equiangular. Tell whether each polygon is regular or irregular. Then tell whether it is concave or convex Find the sum of the interior angle measures of a 14-gon. 9. Find the measure of each interior angle of hexagon EF. 10. Find the value of n in pentagon PQRST. 2

3 Quadrilateral is any 4-sided polygon. The sum of interior angles for every quadrilateral is 360. Kites 2 pairs of congruent consecutive sides (unequal) Te diagonals are perpendicular Rectangles ll properties of parallelogram Four right angles iagonals are congruent & bisect each other onsecutive sides are perpendicular Squares ll properties of the parallelogram, the rectangle and the rhombus Parallelograms Opposite sides are congruent Opposite sides are parallel Opposite angles are congruent onsecutive angles are supplementary The diagonals bisect each other Trapezoids Has only 1 pair of parallel sides (base 1 & base 2) Non-parallel sides are called legs Rhombus ll the properties of parallelogram Four congruent sides onsecutive sides are congruent iagonals bisect opposite angles iagonals perpendicular & bisect each other Example E 12 m< = 27 m< = 38 m< = 63 m< = 52 7 Find each measure. True/False 1. Every parallelogram is a quadrilateral. 2. Every quadrilateral is a parallelogram. 3. ll angles of a parallelogram are congruent. 4. Opposite sides of a parallelogram are always congruent. 5. In PEX, P // PX. 6. In RY, R Y. 7. In TO, T and O bisect each other. 3

4 The following figures are s. 1. Given: O = 2x + 5y S TO = 18 ON = 30 O SO = 2x + 2y Find x and y. T N P S Example 2. Given: mp = 85 mps = 130 mls = (x y) msl = (x + y) oordinate Geometry: Show that (2, -1) (1, 3) (6, 5) and (7, 1) are vertices of a parallelogram. Method 1: Find the slopes (opposite sides should be parallel) L Method 2: Find lengths (opposite sides should be congruent) Method 3: One pair of opposite sides are parallel and congruent Proving a Quadrilateral is a parallelogram quadrilateral is a parallelogram if: 1. both pairs of opposite sides are parallel (by definition)

5 5

6 Rectangles efinition: rectangle is a quadrilateral with. efinition: rectangle is a parallelogram with. Prove the diagonals are in a Rectangle: Given: Rectangle Prove: To Prove that a quadrilateral is a rectangle, prove that: 1) It is a quadrilateral with. 2) It is a parallelogram with. 3) It is a parallelogram with. Find all interior angle measures given rectangle STN. 31 S O Which of the following quadrilaterals are rectangles? Justify your answer N T For 4 10, is a parallelogram. From the information given, tell whether is a rectangle. 4. Given: 5. Given: 6. Given: is a right angle. 7. Given: 8. Given: 9. Given: 10. Given: ; is a right angle 11. Find x and y Given: iagonals RP and SQ of rectangle PQRS meet at M. If PM = x + 3y, SM = 4y 2x and RM = 20. 6

7 Rhombus efinition: quadrilateral is a rhombus iff. efinition: parallelogram is a rhombus iff. H R O Mark the rhombus. How many s? What must be true about HO? Therefore, diagonals must be. Theorem: parallelogram is a rhombus iff. M To Prove that a quadrilateral is a rhombus, prove that: 1) It is a quadrilateral with. 2) It is a parallelogram with. 3) It is a parallelogram with. 4) It is a parallelogram with. 5) Find all interior angles of the following rhombus. 23 6) Given: ZY; ZY X ; 1 2 Prove: ZY is a rhombus X Z Y Which of the following are rhombuses? Justify each answer For 4 10, is a parallelogram. From the info. Given tell whether is a rhombus. 4. Given: 5. Given: 6. Given: is a right angle 7. Given: 8. Given: ; is a right angle 9. Given: 10. Given: 11. In rhombus, m = 3x 5 and m = 11x 3. Find the measures of all the angles of the rhombus. 12. In parallelogram, = 17x 3, = 13x + 5, and = 4x Find the lengths of the sides of parallelogram. What type of parallelogram is? 7

8 PROOFS: 1. Given: Rhombus ; FE // Prove: EF E F 2. Given: Rhombus Prove:

9 parallelogram is a square iff it has one right angle and 2 adjacent sides. square is both a and a. square has all of the properties of a,, and. To prove a quadrilateral is a square, prove that: 1) It is a rectangle with. 2) It is a rectangle with. 3) It is a rectangle with. 4) It is a rhombus with. 5) It is a rhombus with. 6) It is a parallelogram with. omplete the following. 1. Every rectangle is also a. 2. Every rhombus is also a. 3. Every square is also a, and a. 4. with diagonals is a or a. 5. with diagonals is a or a. 6. whose diagonals are the bisectors of each other is a or a. True or False. 7. ll rhombi are parallelograms. 8. Some rectangles are squares. 9. ll parallelograms are rectangles. 10. Some rhombi are rectangles. 11. ll rectangles are squares. 12. ll squares are rectangles. 13. Some squares are rectangles. 14. Given: Square HIJK and equilateral ILJ. Find mhli. H I L 15. In Square, diagonals and meet at E. Find m. K J 16. The rectangle to the right is divided in squares. The 2 largest are 69 and 72 units on a side. How long is each side of each square? Use square and the given information to find each value. 14. If me = 3x, find x. 15. If m = 9x, find x. 16. If = 2x + 1 and = 3x 5, find 17. If m = y and m = 3x, find x and y. 18. If = x 2-15 and = 2x, find x E 9

10 6.6 Kites and Trapezoids y 6x 3x 2 Find the value(s) of the variable(s) in each kite (3x+5) 1 6 (x+6) 15y (2x-4) y (4x- 30) (2y-20) x an two angles of a kite be as follows? 7. opposite and acute 8. consecutive and obtuse 9. opposite and supplementary 10. consecutive and supplementary 11. opposite and complementary 12. consecutive and complementary 13. The perimeter of a kite is 66 cm. The length of one of its sides is 3 cm less that twice the length of another. Find the length of each side of the kite. 14. etermine whether the points (4, 5), (-3, 3), (-6, -13) and (6, -2) are the vertices of a kite. Show your work. Trapezoids efinition: trapezoid is a quadrilateral with exactly two parallel sides. Parts of a trapezoid: Leg ase Leg ase Leg 10 ase Leg ase

11 Isosceles Trapezoid: trapezoid with congruent legs. Every trapezoid contains two pairs of consecutive angles that are supplementary. Example 1: Given the trapezoid HLJK H L If the m J 65 and the K J m K 95, the measure of angles H and L. Theorem: The base angles of an isosceles trapezoid are congruent. Theorem: The diagonals of an isosceles trapezoid are congruent. Example 2: Use Isosceles Trapezoid with length of =. // a. m = 75. Find the m. b. = 40. Find. c. If m 6x 25 and m 8x 15, find the measures of angle and. efinition: m altitude is a line segment from one vertex of one base of the trapezoid and perpendicular to the opposite base. Theorem: The length of the median of a trapezoid equals one-half the sum of the bases. m Example 3: Find the missing measures of the given trapezoid. 1 2 b 1 b 2 7 I a. mir b. YR c. R d X Y R

12 Example 4: HJKL is an isosceles trapezoid with bases HJ and LK, and median RS. Use the given information to solve each problem. a. LK = 30 find LK L K HJ = 42 find RS c. RS = x + 5 R S b. RS = 17 HJ = 14 HJ + LK = 4x + 6 find RS H J Example 5: 5x + 12 Find the length of each side of the isosceles trapezoid below. 6x x 14x 12

13 TRPEZOI PRTIE I. Fill in the blanks: 1) trapezoid is a quadrilateral with exactly one pair of _?_ opposite sides. 2) If the non-parallel sides of a trapezoid are, then it is called a(n) _?_ trapezoid. 3) The parallel sides of a trapezoid are called its _? 4) nd the non-parallel sides are called the _? 5) The segment that joins the midpoints of the non-parallel sides of a trapezoid is called the _? 6) and is parallel to the _?_ of the trapezoid. II. nswer the following. Show your work to get credit. 7) 8) 9) x x y 9x z 3x-5 x = x = y = x = z = m = m = 10 x 10) 11) 12) x x w y z w = x = x = x = y = 13

14 LWYS, SOMETIMES, OR NEVER Part The diagonals of a quadrilateral bisect each other. 2. If the measures of 2 angles of a quadrilateral are equal, then the quadrilateral is a parallelogram. 3. If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is a parallelogram. 4. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 5. To prove a quadrilateral is a parallelogram, it is enough to show that one pair of opposite sides is parallel. 6. The diagonals of a rectangle are congruent. 7. The diagonals of a parallelogram bisect the angles. Part 2. always-sometimes-never 1. square is a rhombus. 2. The diagonals of a parallelogram bisect the angles of the parallelogram. 3. quadrilateral with one pair of sides congruent and one pair parallel is a parallelogram. 4. The diagonals of a rhombus are congruent. 5. rectangle has consecutive sides congruent. 6. rectangle has perpendicular diagonals. 7. The diagonals of a rhombus bisect each other. 8. The diagonals of a parallelogram are perpendicular bisectors of each other. 14

15 15

16 Square wksht Property 1. It has Four Sides 2. Opposite Sides are Parallel 3. Opposite Sides are ongruent 4. Opposite ngles are ongruent 5. iagonals isect Each Other 6. iagonal Forms Two ongruent Triangles 7. iagonals are ongruent 8. iagonals are Perpendicular to each other 9. iagonal isects Two Opposite ngles 10. ll ngles are Right ngles 11. ll Sides are ongruent 12. Two Sides are ongruent and djacent 13. onsecutive ngles re Supplementary 14. onsecutive angles are congruent. 15. It is equilateral. 16. It is equiangular. 17. onsecutive (adjacent) sides are perpendicular. 18.iagonals are congruent, perpendicular, and bisect each other. lgebraic Formulas Used to etermine the Type of Quadrilateral Quadrilateral Parallelogram Rectangle Rhombus Square istance Formula-**use to determine if opposite sides are 2 2 d x x y y Midpoint Formula **use to determine if diagonals bisect each other(they have to have the some midpoint) x x y y, Slope Formula-**use to determine if opposite sides are parallel m y x 2 2 y 1 x 1 Honors Geometry oordinate onnection Notes 16

17 To Show that a quadrilateral is a Parallelogram Method 1: oth pairs of opposite sides are congruent (find distance) Method 2: oth pairs of opposite sides are parallel (find slope) Method 3: One pair of opposite sides are both parallel and congruent (find distance and slope) To show that a quadrilateral is a Rhombus ****FIRST show that it is a parallelogram**** Method 1: ll 4 sides are congruent Method 2: iagonals are perpendicular (find slope of diagonals) To show that a quadrilateral is a Rectangle ****FIRST show that it is a parallelogram**** Method 1: ll angles are right angles Method 2: iagonals are congruent (find distance of diagonals) To show that a quadrilateral is an Isosceles Trapezoid Graph first o Legs are congruent (find distance) o ases are parallel (find slope) iagonals are congruent To show that a quadrilateral is a Kite Graph first o Two pairs of consecutive congruent sides that are not congruent to each other (find the distance) Honors Geometry oordinate onnection 1. Given: (-1,-6), (1,-3), (11,1) and (9,-2) Show that Quad. is a parallelogram. 2. Given: E(-4,1), F(2,3), G(4,9) and H(-2,7) a) Show that EFGH is a rhombus. b) Use slopes to verify that the diagonals are perpendicular. 3. Given: R(-4,5), S(-1,9), T(7,3) and U(4,-1) a) Show that RSTU is a rectangle. b) Use the distance formula to verify that the diagonals are. 4. Given: N(-1,-5), O(0,0), P(3,2) and Q(8,1) a) Show that NOPQ is an isosceles trapezoid. b) Show that the diagonals are. More examples: 1. Given: with (2,6), (3,-5), and (-1,7). If M is the midpoint of and N is the midpoint of, show MN //. 2. Given: Trapezoid with (4,0), (8,0), (0,2) and (0,4). Find the length of the median. 3. Given: Rectangle with (6,-4), (6,2), (3,2) and (3,-4). Write the equations of the lines that contain the diagonals in standard form. 4. Given: Quad. with (3.2), (8,1), (7,6) and (2,7). What name best describes the quadrilateral? Prove (explain) your answer. 5. RHOM is a rhombus. R(1,3), M(14,3), H(6,15) a) Find the coordinate of O. b) Find the slopes of HM and RO. c) What does part b verify? H O 17 R M

### 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.

### 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

### 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

### 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

Unit 8 Quadrilaterals Academic Geometry Spring 2014 Name Teacher Period 1 2 3 Unit 8 at a glance Quadrilaterals This unit focuses on revisiting prior knowledge of polygons and extends to formulate, test,

### 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

### 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

### 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?

### 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

### 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

### 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:

### 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

### 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

### Final Review Geometry A Fall Semester

Final Review Geometry Fall Semester Multiple Response Identify one or more choices that best complete the statement or answer the question. 1. Which graph shows a triangle and its reflection image over

### 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,

### 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

### 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

### 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

HPTER QURILTERLS Euclid s fifth postulate was often considered to be a flaw in his development of geometry. Girolamo Saccheri (1667 1733) was convinced that by the application of rigorous logical reasoning,

### 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.

### 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

### 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

### GEOMETRY FINAL EXAM REVIEW

GEOMETRY FINL EXM REVIEW I. MTHING reflexive. a(b + c) = ab + ac transitive. If a = b & b = c, then a = c. symmetric. If lies between and, then + =. substitution. If a = b, then b = a. distributive E.

### 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

### 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

### Su.a Supported: Identify Determine if polygons. polygons with all sides have all sides and. and angles equal angles equal (regular)

MA.912.G.2 Geometry: Standard 2: Polygons - Students identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. They find measures

### 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

### A summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs:

summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: efinitions: efinition of mid-point and segment bisector M If a line intersects another line segment

### 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:

### 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

# 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

### (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

### 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,

### 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:

### Polygons in the Coordinate Plane. isosceles 2. X 2 4

Name lass ate 6-7 Practice Form G Polgons in the oordinate Plane etermine whether k is scalene, isosceles, or equilateral. 1. isosceles. scalene 3. scalene. isosceles What is the most precise classification

### 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

### 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

### 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

### 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

### 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

### 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

### **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:

### Lesson 3.1 Duplicating Segments and Angles

Lesson 3.1 Duplicating Segments and ngles In Exercises 1 3, use the segments and angles below. Q R S 1. Using only a compass and straightedge, duplicate each segment and angle. There is an arc in each

### A summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs:

summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: efinitions: efinition of mid-point and segment bisector M If a line intersects another line segment

### 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

### 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

### Geometry Final Assessment 11-12, 1st semester

Geometry Final ssessment 11-12, 1st semester Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Name three collinear points. a. P, G, and N c. R, P, and G

### 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

### Area. Area Overview. Define: Area:

Define: Area: Area Overview Kite: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: Postulates/Theorems: Every closed region has an area. If closed figures are congruent, then their areas are equal.

### 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

### 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,

### 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,

### 1.2 Informal Geometry

1.2 Informal Geometry Mathematical System: (xiomatic System) Undefined terms, concepts: Point, line, plane, space Straightness of a line, flatness of a plane point lies in the interior or the exterior

### 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

### GEOMETRY CONCEPT MAP. Suggested Sequence:

CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons

### Given: ABCD is a rhombus. Prove: ABCD is a parallelogram.

Given: is a rhombus. Prove: is a parallelogram. 1. &. 1. Property of a rhombus. 2.. 2. Reflexive axiom. 3.. 3. SSS. + o ( + ) =180 4.. 4. Interior angle sum for a triangle. 5.. 5. PT + o ( + ) =180 6..

### NCERT. In examples 1 and 2, write the correct answer from the given four options.

MTHEMTIS UNIT 2 GEOMETRY () Main oncepts and Results line segment corresponds to the shortest distance between two points. The line segment joining points and is denoted as or as. ray with initial point

### GEOMETRIC FIGURES, AREAS, AND VOLUMES

HPTER GEOMETRI FIGURES, RES, N VOLUMES carpenter is building a deck on the back of a house. s he works, he follows a plan that he made in the form of a drawing or blueprint. His blueprint is a model of

### 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

### 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

### 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 +

### 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.

### 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

### /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

### 1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?

1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width

### 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

### Name Geometry Exam Review #1: Constructions and Vocab

Name Geometry Exam Review #1: Constructions and Vocab Copy an angle: 1. Place your compass on A, make any arc. Label the intersections of the arc and the sides of the angle B and C. 2. Compass on A, make

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

### 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.

### 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

### *1. Understand the concept of a constant number like pi. Know the formula for the circumference and area of a circle.

Students: 1. Students deepen their understanding of measurement of plane and solid shapes and use this understanding to solve problems. *1. Understand the concept of a constant number like pi. Know the

### Cumulative Test. 161 Holt Geometry. Name Date Class

Choose the best answer. 1. P, W, and K are collinear, and W is between P and K. PW 10x, WK 2x 7, and PW WK 6x 11. What is PK? A 2 C 90 B 6 D 11 2. RM bisects VRQ. If mmrq 2, what is mvrm? F 41 H 9 G 2

### 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

### 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

### 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.

### 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

### 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

### PARALLEL LINES CHAPTER

HPTR 9 HPTR TL OF ONTNTS 9-1 Proving Lines Parallel 9-2 Properties of Parallel Lines 9-3 Parallel Lines in the oordinate Plane 9-4 The Sum of the Measures of the ngles of a Triangle 9-5 Proving Triangles

### Geometry Honors: Circles, Coordinates, and Construction Semester 2, Unit 4: Activity 24

Geometry Honors: Circles, Coordinates, and Construction Semester 2, Unit 4: ctivity 24 esources: Springoard- Geometry Unit Overview In this unit, students will study formal definitions of basic figures,

### 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.

### 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

### Geometry Chapter 1 Vocabulary. coordinate - The real number that corresponds to a point on a line.

Chapter 1 Vocabulary coordinate - The real number that corresponds to a point on a line. point - Has no dimension. It is usually represented by a small dot. bisect - To divide into two congruent parts.

### 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

### 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

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

### Identifying Triangles 5.5

Identifying Triangles 5.5 Name Date Directions: Identify the name of each triangle below. If the triangle has more than one name, use all names. 1. 5. 2. 6. 3. 7. 4. 8. 47 Answer Key Pages 19 and 20 Name

### b. Create a graph to show how far Maggie and Mike can travel based on the chart above.

Final Exam Review 1. Find the midpoint, the distance and the slope between (4,-2) and (-5, 3) 2. Jacinta hangs a picture 15 inches from the left side of a wall. How far from the edge of the wall should

### Selected practice exam solutions (part 5, item 2) (MAT 360)

Selected practice exam solutions (part 5, item ) (MAT 360) Harder 8,91,9,94(smaller should be replaced by greater )95,103,109,140,160,(178,179,180,181 this is really one problem),188,193,194,195 8. On

### 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.

### 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,

### 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

### Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Name: lass: _ ate: _ I: SSS Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Given the lengths marked on the figure and that bisects E, use SSS to explain

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

### 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

### 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

### 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

### Student Name: Teacher: Date: District: Miami-Dade County Public Schools. Assessment: 9_12 Mathematics Geometry Exam 1

Student Name: Teacher: Date: District: Miami-Dade County Public Schools Assessment: 9_12 Mathematics Geometry Exam 1 Description: GEO Topic 1 Test: Tools of Geometry Form: 201 1. A student followed the