Geometry 81 Angles of Polygons


 Gabriella Jacobs
 2 years ago
 Views:
Transcription
1 . Sum of Measures of Interior ngles Geometry 81 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. 2. Theorem 81 (Interior angle sum Theorem) If a convex polygon has n sides and S is the sum of the measures of the interior angles, then S = 180(n  2). onvex Polygon # of sides # of Vs Sum of ngle Measures triangle 3 1 (1 180) or 180 quadrilateral 4 2 (2 180) or 360 pentagon 5 3 (3 180) or 540 hexagon 6 4 (4 180) or 720 heptagon 7 5 (5 180) or 900 octagon 8 6 (6 180) or 1080 Ex 1: Find the measure of each interior angle of a regular pentagon. Use the interior angle sum theorem to find the sum of the angle measures. S = 180(n  2) S = 180(  2) S = so each angle is /5 or. Ex 2: Find the measure of each interior angle. R (11x + 4) o S 5x o U 5x o (11x + 4) o T. Sum of Measures of Exterior ngles x x x x x
2 1. Theorem 82 Exterior ngle Sum Theorem  If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex is 360. (exterior angle)(# of sides) = 360 Ex 3: Find the measures of an exterior and interior angle for a regular hexagon. HW: Geometry 81 p odd, odd 4748, odd, odd Hon: 57
3 Geometry 82 Parallelograms. Sides and angles of parallelograms 1. quadrilateral with opposite sides is called a parallelogram. Y. Theorems 1. Theorem 83 Opposite sides of a parallelogram are congruent abbreviation: Opp. sides of Y are. 2. Theorem 84 Opposite angles of a parallelogram are congruent abbreviation: Opp. s of Y are. 3. Theorem 85 onsecutive angles of a parallelogram are supplementary. abbreviation: ons. s of Y are suppl. 4. Theorem 86 If a parallelogram has one right angle, it has 4 right angles. abbreviation: If Y has 1 rt., it has 4 rt. s. Ex. 1: Write a 2 column proof for Theorem 84 Given: Y Prove:, Statements Reasons 1. Y 1. Given 2., and are supplementary 3. and are supplementary and are supplementary 4., 4.
4 Ex. 2: RSTU is a parallelogram, find m URT, m RST, and y. R U 3y S 18 o 40o 18 T. iagonals of Parallelograms R S 1. Theorem 87 The diagonals of a parallelogram bisect each other. So: RQ QT and U Q T Ex: 3: What are the coordinates of the intersection of the diagonals of parallelogram MNPR with vertices M(3, 0), N(1, 3), P(5, 4), R(3, 1). 2. Theorem 88 Each diagonal of a parallelogram separates the parallelogram into two congruent triangles. abbreviation: iag. separates Y into 2 V s. HW: Geometry 82 p all, 3739, 5051, odd, 5657, odd Hon: 36, 46 Geometry 83 Tests for Parallelograms. onditions for a parallelogram
5 1. Theorem If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. abbreviation: If both pairs of opp. sides are, then quad. is Y. 2. Theorem If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. abbreviation: If both pairs of opp. 's are, then quad. is Y. 3. Theorem If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. abbreviation: If diag. bisect each other, then quad. is Y. 4. Theorem If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram. abbreviation: If one pair of opp sides is and, then quad. is Y. Ex 1: etermine whether the quadrilateral is a parallelogram Ex 2: Find x and y so that each quadrilateral is a parallelogram. a.) E 8y 15 F 6x 12 2x + 16 b.) H o (5y + 283) y + 10 (6y + 14 o ) G
6 . Parallelograms and the oordinate Plane You can use the istance Formula (or Pythagorean Theorem) to determine if a quadrilateral is a parallelogram in the coordinate plane. Ex 3: The coordinates of the vertices of a quadrilateral PQRS are P(5,3), Q(1,5), R(6,1) and S(2,1). etermine if quadrilateral PQRS is a parallelogram. quadrilateral is a parallelogram if and only if any one of the following is true: 1. oth pairs of opposite sides are parallel. (efinition) 2. oth pairs of opposite sides are congruent. (Theorem 89) 3. iagonals bisect each other. (Theorem 810) 4. oth pairs of opposite angles are congruent (Theorem 811) 5. pair of opposite sides is both parallel and congruent (Theorem 812) HW: Geometry 83 p , odd, 37, 4550, odd Hon: 2324, 33, 35, 39 Geometry 84 Rectangles. Properties of Rectangles
7 1. efinition  rectangle is a quadrilateral with four right angles. if both pairs of opposite angles are congruent, then it is a parallelogram.  Thus a rectangle is a parallelogram. M 2. Theorem 813 If a parallelogram is a rectangle, then its diagonals are congruent. abbreviation: if Y is a rectangle, diag. are. Ex 1: Quadrilateral RSTU is a rectangle. If RT = 6x + 4, and SU = 7x 4, find x. R U S T Ex 2: Find x and y if MNPL is a rectangle. M 6 y + 2 o N L 5x + 8 o 3x + 2 o P 3. Theorem 814 If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. Ex. 3: etermine whether parallelogram is a rectangle, given (2, 1), (4, 3), (5, 0), and (1, 2).
8 HW: Geometry 84 p odd, Hon: 42 Geometry 85 Rhombi and Squares M. Properties of Rhombi 1. rhombus is a quadrilateral with all 4
9 sides congruent. 2. Theorem The diagonals of a rhombus are perpendicular. and 3. Theorem If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. 4. Theorem Each diagonal of a rhombus bisects a pair of opposite angles. so and M Ex 1: a.) Find y if 2 m 1 y 10. = L 1 Q N b.) Find m PNL if m MPL = 64. P Ex 2: etermine whether parallelogram is a rhombus, a rectangle, or a square for (4, 2), (2, 6) (6, 4), (4, 4). List all that apply. (2, 6) (6, 4) (4, 2) (4, 4) Ex 3: square table has four legs that are 2 feet apart. The table is placed over an umbrella stand so that the hole in the center of the table lines up with the hole in the stand. How far away from a leg is the center of the hole?
10 Properties of Rhombi and Squares Rhombi Squares 1. rhombus has all the properties of a 1. square has all the properties of a parallelogram. parallelogram 2. ll sides are congruent. 2. square has all the properties of a rectangle. 3. iagonals are perpendicular. 3. square has all the properties of a rhombus. 4. iagonals bisect the angles of the rhombus. HW: Geometry 85 p , 2123, 2631, 32, 4647, odd Hon: 37, 38, 40, 42, 44 Geometry 86 Trapezoids. Properties of Trapezoid 1. trapezoid is a quadrilateral with exactly one pair of parallel sides. 2. The parallel sides are called bases. 3. The base angles are formed by the base and one of the legs. 4. The nonparallel sides are called legs. base
11 5. If the legs are congruent, then the trapezoid is an isosceles trapezoid. 6. Theorem oth pairs of base angles of an isosceles trapezoid are congruent. 7. Theorem The diagonals of an isosceles trapezoid are congruent. Ex 1: Finish the flow proof of Theorem Given: MNOP is an isosceles trapezoid Prove: MO NP Proof: M N P O MNOP is an isosceles V MP NO MPO NOP PO PO Ex 2: is a quadrilateral with vertices (5, 1), (3, 1), (2, 3), and (2, 4). a.) Verify that is a trapezoid.
12 b.) etermine whether is an isosceles trapezoid. Explain.. Medians of Trapezoids 1. The segment that joins midpoints of the legs of a trapezoid is the median. (sometimes called the midsegment) 2. Theorem The median of a trapezoid is parallel to the bases and its measure is onehalf the sum of the bases. 1 Ex: MN = ( + ) 2 Ex 3: EFG is an isosceles trapezoid with median MN. a.) Find G if EF = 20 and MN = 30. M N E 3 4 M N 1 2 G b.) Find m 1, m 2, m 3, and m 4 if m 1 = 3x + 5 and m 3 = 6x 5. HW: Geometry 86 p odd, 1318, 2228, 4248, odd Hon: 19, 20, 32, 35 Geometry 87 oordinate Proof With Quadrilaterals. Position Figures Ex 1: Position and label a square with sides a units long on the coordinate plane. 1.) Let,,, and be the vertices of the square. (0, ) (, ) (0, 0) (, 0)
13 2.) Place the square with vertex at the origin, along the positive xaxis, and along the yaxis. Label the vertices,, and. 3.) The ycoordinate of is 0 because the vertex is on the xaxis. Since the side length is a, the xcoordinate is. 4.) is on the yaxis so the xcoordinate is 0. The ycoordinate is 0 + a or. 5.) The xcoordinate of is also. The ycoordinate is 0 + a, or because side is a units long. Ex 2: Name the missing coordinate for the isosceles trapezoid. (?,?) (a2b, c) (0, 0) (a, 0). Prove Theorems 1. Once we have place a figure on the coordinate plane, we can use slope formula, distance formula and midpoint formula to prove theorems. Ex 3: Place a square on the coordinate plane. Label the midpoints of the sides, M, N, P, and Q. Write a coordinate proof to show MNPQ is a square. a.) y midpoint formula, the coordinates of M, N, O, and P are as follows: M (, ) N (, ) P (, ) Q (, ) (0, 2a) (2a, 2a) b.) Find the slopes of QP, MN, QM, and PN. (0, 0) (2a, 0)
14 Each pair of opposite sides is, therefore MNPQ is a, and a c.) Use the distance formula to find QP and QM. MNPQ is a square because each pair of opposite sides is parallel, and consecutive sides form and are. HW: Geometry 87 p , 2425, 2839
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(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 informationSum of the interior angles of a nsided Polygon = (n2) 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 nsided Polygon = (n2) 180 What you need to know: How to use the formula
More informationGeo  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 informationUnit 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 informationUnit 8. Quadrilaterals. Academic Geometry Spring Name Teacher Period
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,
More information8.1 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 informationM 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 informationAlgebra 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 informationUnit 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 informationCHAPTER 6. Polygons, Quadrilaterals, and Special Parallelograms
CHAPTER 6 Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 61) SWBAT: Find measures of interior and exterior angles of polygons Pgs: 17 HW: Pgs: 810 DAY 2: (62) Pgs:
More informationHonors Packet on. Polygons, Quadrilaterals, and Special Parallelograms
Honors Packet on Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 61) SWBAT: Find measures of interior and exterior angles of polygons Pgs: #1 6 in packet HW: Pages 386
More informationPolygons 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 information1. 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 informationChapters 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 informationQUADRILATERALS CHAPTER
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,
More informationA. Areas of Parallelograms 1. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh.
Geometry  Areas of Parallelograms A. Areas of Parallelograms. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh. A B Ex: See how VDFA V CGB so rectangle
More informationPolygons in the Coordinate Plane. isosceles 2. X 2 4
Name lass ate 67 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
More information65 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 information11.3 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 information56 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 informationConjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C2 Vertical Angles Conjecture If two angles are vertical
More informationLine. 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 informationQuadrilaterals 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 informationINDEX. Arc Addition Postulate,
# 3060 right triangle, 441442, 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 information65 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 twocolumn proof to prove that if ABCD is a rhombus with diagonal. 1. If, find. A rhombus is a parallelogram with all
More informationparallel 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 informationA 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 informationQuadrilaterals 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 informationGeometry 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 informationTarget To know the properties of a rectangle
Target To know the properties of a rectangle (1) A rectangle is a 3D 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 informationFinal 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 3x6. Find the measure of the angles. State the theorem(s) that support your equation.
More information**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 informationName 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
More informationGeometry Regents Review
Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest
More informationQuadrilaterals 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(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 informationName: 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 informationGEOMETRY 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.
More informationFinal 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
More informationConjectures 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 informationacute angle acute triangle Cartesian coordinate system concave polygon congruent figures
acute angle acute triangle Cartesian coordinate system concave polygon congruent figures convex polygon coordinate grid coordinates dilatation equilateral triangle horizontal axis intersecting lines isosceles
More informationGeometry 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 informationCONJECTURES  Discovering Geometry. Chapter 2
CONJECTURES  Discovering Geometry Chapter C1 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 information63 Tests for Parallelograms. Determine whether each quadrilateral is a parallelogram. Justify your answer.
1. Determine whether each quadrilateral is a Justify your answer. 3. KITES Charmaine is building the kite shown below. She wants to be sure that the string around her frame forms a parallelogram before
More information/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 informationGEOMETRY 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 (x₂x₁)²+(y₂y₁)² Find the distance between the points ( 3,2) and
More informationGiven: 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..
More information15 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 information7.3 & 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 informationSituation: 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 informationBASIC 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 information39 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 informationThe 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 informationGeometry Vocabulary. Created by Dani Krejci referencing:
Geometry Vocabulary Created by Dani Krejci referencing: http://mrsdell.org/geometry/vocabulary.html point An exact location in space, usually represented by a dot. A This is point A. line A straight path
More informationDefinitions, 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 informationDate: 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 informationContent 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 informationLEVEL 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 informationCentroid: 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 informationSOLVED PROBLEMS REVIEW COORDINATE GEOMETRY. 2.1 Use the slopes, distances, line equations to verify your guesses
CHAPTER SOLVED PROBLEMS REVIEW COORDINATE GEOMETRY For the review sessions, I will try to post some of the solved homework since I find that at this age both taking notes and proofs are still a burgeoning
More information1 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 informationUnit 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 informationTABLE OF CONTENTS. Free resource from Commercial redistribution prohibited. Understanding Geometry Table of Contents
Understanding Geometry Table of Contents TABLE OF CONTENTS Why Use This Book...ii Teaching Suggestions...vi About the Author...vi Student Introduction...vii Dedication...viii Chapter 1 Fundamentals of
More informationChapter 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 informationPOLYGONS
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, twodimensional figure made of three or more nonintersecting straight
More informationPostulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.
Chapter 11: Areas of Plane Figures (page 422) 111: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length
More informationTopics 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 informationNovember 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 informationNCERT. 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
More information104 Inscribed Angles. Find each measure. 1.
Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semicircle. 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 informationAngles 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 informationINFORMATION 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 informationDEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.
DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent
More informationChapter 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 informationArea. 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.
More informationA Different Look at Trapezoid Area Prerequisite Knowledge
Prerequisite Knowledge Conditional statement an ifthen 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 informationGeometry Final Assessment 1112, 1st semester
Geometry Final ssessment 1112, 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
More informationPOTENTIAL REASONS: Definition of Congruence:
Sec 6 CC Geometry Triangle Pros Name: POTENTIAL REASONS: Definition Congruence: Having the exact same size and shape and there by having the exact same measures. Definition Midpoint: The point that divides
More informationIdentifying 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
More informationof surface, 569571, 576577, 578581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433
Absolute Value and arithmetic, 730733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property
More informationCoordinate Coplanar Distance Formula Midpoint Formula
G.(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the oneand twodimensional coordinate systems to
More informationUNIT 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 information1. 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
More informationMATH 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 informationChapter 1 Line and Angle Relationships
Chapter 1 Line and Angle Relationships SECTION 1.1: Sets, Statements, and Reasoning 1. a. Not a statement. b. Statement; true c. Statement; true d. Statement; false. a. Statement; true b. Not a statement.
More information1. point, line, and plane 2a. always 2b. always 2c. sometimes 2d. always 3. 1 4. 3 5. 1 6. 1 7a. True 7b. True 7c. True 7d. True 7e. True 8.
1. point, line, and plane 2a. always 2b. always 2c. sometimes 2d. always 3. 1 4. 3 5. 1 6. 1 7a. True 7b. True 7c. True 7d. True 7e. True 8. 3 and 13 9. a 4, c 26 10. 8 11. 20 12. 130 13 12 14. 10 15.
More informationFind the sum of the measures of the interior angles of a polygon. Find the sum of the measures of the exterior angles of a polygon.
ngles of Polygons Find the sum of the measures of the interior angles of a polygon. Find the sum of the measures of the exterior angles of a polygon. Vocabulary diagonal does a scallop shell illustrate
More informationSelected 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
More informationSect 8.3 Quadrilaterals, Perimeter, and Area
186 Sect 8.3 Quadrilaterals, Perimeter, and Area Objective a: Quadrilaterals Parallelogram Rectangle Square Rhombus Trapezoid A B E F I J M N Q R C D AB CD AC BD AB = CD AC = BD m A = m D m B = m C G H
More informationABC 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 informationGEOMETRY 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
More informationChapter 6 Notes: Circles
Chapter 6 Notes: Circles IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of the circle. Any line segment
More informationA 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 midpoint and segment bisector M If a line intersects another line segment
More informationThe Parallelogram REMEMBER A parallelogram is a quadrilateral with opposite sides parallel. It has many special properties.
ame: Date: The Parallelogram REMEMBER A parallelogram is a quadrilateral with opposite sides parallel. It has many special properties. If you are given parallelogram ABCD then: Property Meaning (1) opposite
More information4.1 Euclidean Parallelism, Existence of Rectangles
Chapter 4 Euclidean Geometry Based on previous 15 axioms, The parallel postulate for Euclidean geometry is added in this chapter. 4.1 Euclidean Parallelism, Existence of Rectangles Definition 4.1 Two distinct
More informationChapter 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 informationEND OF COURSE GEOMETRY CORE 1
SESSION: 24 PE: 1 5/5/04 13:29 OIN ISglenn PT: @sunultra1/raid/s_tpc/rp_va_sprg04/o_04ribsg11/iv_g11geom1 VIRINI STNRS O ERNIN SSESSMENTS Spring 2004 Released Test EN O OURSE EOMETRY ORE 1 Property
More informationConjunction is true when both parts of the statement are true. (p is true, q is true. p^q is true)
Mathematical Sentence  a sentence that states a fact or complete idea Open sentence contains a variable Closed sentence can be judged either true or false Truth value true/false Negation not (~) * Statement
More information61 Properties and Attributes of Polygons
61 Properties and Attributes of Polygons Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up 1. A? is a threesided polygon. triangle 2. A? is a foursided polygon. quadrilateral Evaluate each expression
More information