# Properties of Rhombuses, Rectangles, and Squares

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 8.4 roperties of hombuses, ectangles, and quares efore You used properties of parallelograms. Now You will use properties of rhombuses, rectangles, and squares. Why? o you can solve a carpentry problem, as in Example 4. Key Vocabulary rhombus rectangle square In this lesson, you will learn about three special types of parallelograms: rhombuses, rectangles, and squares. rhombus is a parallelogram with four congruent sides. rectangle is a parallelogram with four right angles. square is a parallelogram with four congruent sides and four right angles. You can use the corollaries below to prove that a quadrilateral is a rhombus, rectangle, or square, without first proving that the quadrilateral is a parallelogram. OOLLIE For Your Notebook HOMU OOLLY quadrilateral is a rhombus if and only if it has four congruent sides. is a rhombus if and only if } > } > } > }. roof: Ex. 57, p. 539 ENGLE OOLLY quadrilateral is a rectangle if and only if it has four right angles. is a rectangle if and only if,,, and are right angles. roof: Ex. 58, p. 539 QUE OOLLY quadrilateral is a square if and only if it is a rhombus and a rectangle. is a square if and only if } > } > } > } and,,, and are right angles. roof: Ex. 59, p roperties of hombuses, ectangles, and quares 533

3 IGONL he theorems below describe some properties of the diagonals of rhombuses and rectangles. HEOEM For Your Notebook HEOEM 8.11 parallelogram is a rhombus if and only if its diagonals are perpendicular. ~ is a rhombus if and only if } }. roof: p. 536; Ex. 56, p. 539 HEOEM 8.12 parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles. ~ is a rhombus if and only if } bisects and and } bisects and. roof: Exs , p. 539 HEOEM 8.13 parallelogram is a rectangle if and only if its diagonals are congruent. ~ is a rectangle if and only if } > }. roof: Exs , p. 540 E X M L E 3 List properties of special parallelograms ketch rectangle. List everything that you know about it. olution y definition, you need to draw a figure with the following properties: he figure is a parallelogram. he figure has four right angles. ecause is a parallelogram, it also has these properties: Opposite sides are parallel and congruent. Opposite angles are congruent. onsecutive angles are supplementary. iagonals bisect each other. y heorem 8.13, the diagonals of are congruent. at classzone.com GUIE IE for Example 3 3. ketch square Q. List everything you know about the square. 8.4 roperties of hombuses, ectangles, and quares 535

4 IONIIONL ecall that biconditionals such as heorem 8.11 can be rewritten as two parts. o prove a biconditional, you must prove both parts. onditional statement If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. onverse If a parallelogram is a rhombus, then its diagonals are perpendicular. O O F art of heorem 8.11 OVE HEOEM You will prove the other part of heorem 8.11 in Exercise 56 on page 539. If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. GIVEN c is a parallelogram; } } OVE c is a rhombus. X roof is a parallelogram, so } and } bisect each other, and }X > } X. lso, X and X are congruent right angles, and } X > } X. o, nx > nx by the ongruence ostulate. orresponding parts of congruent triangles are congruent, so } > }. Opposite sides of a ~ are congruent, so } > } > } > }. y definition, is a rhombus. E X M L E 4 olve a real-world problem ENY You are building a frame for a window. he window will be installed in the opening shown in the diagram. a. he opening must be a rectangle. Given the measurements in the diagram, can you assume that it is? Explain. b. You measure the diagonals of the opening. he diagonals are 54.8 inches and 55.3 inches. What can you conclude about the shape of the opening? olution a. No, you cannot. he boards on opposite sides are the same length, so they form a parallelogram. ut you do not know whether the angles are right angles. b. y heorem 8.13, the diagonals of a rectangle are congruent. he diagonals of the quadrilateral formed by the boards are not congruent, so the boards do not form a rectangle. GUIE IE for Example 4 4. uppose you measure only the diagonals of a window opening. If the diagonals have the same measure, can you conclude that the opening is a rectangle? Explain. 536 hapter 8 Quadrilaterals

5 8.4 EXEIE KILL IE HOMEWOK KEY 5 WOKE-OU OLUION on p. W1 for Exs. 7, 15, and 55 5 NIZE E IE Exs. 2, 30, 31, and VOULY What is another name for an equilateral rectangle? W X 2. WIING o you have enough information to identify the figure at the right as a rhombus? Explain. Z Y EXMLE 1, 2, and 3 on pp for Exs HOMUE For any rhombus JKLM, decide whether the statement is always or sometimes true. raw a diagram and explain your reasoning. 3. L > M 4. K > M 5. } JK > } KL 6. } JM > } KL 7. } JL > } KM 8. JKM > LKM ENGLE For any rectangle WXYZ, decide whether the statement is always or sometimes true. raw a diagram and explain your reasoning. 9. W > X 10. } WX > } YZ 11. } WX > } XY 12. } WY > } XZ 13. } WY } XZ 14. WXZ > YXZ LIFYING lassify the quadrilateral. Explain your reasoning UING OEIE ketch rhombus UV. escribe everything you know about the rhombus. UING OEIE Name each quadrilateral parallelogram, rectangle, rhombus, and square for which the statement is true. 19. It is equiangular. 20. It is equiangular and equilateral. 21. Its diagonals are perpendicular. 22. Opposite sides are congruent. 23. he diagonals bisect each other. 24. he diagonals bisect opposite angles. 25. EO NLYI Quadrilateral Q is a rectangle. escribe and correct the error made in finding the value of x. (7x 4) Q (3x + 14) 7x x x 5 18 x roperties of hombuses, ectangles, and quares 537

6 LGE lassify the special quadrilateral. Explain your reasoning. hen find the values of x and y. 26. y y 1048 x8 x 1 31 K 4y 1 5 L 5x 2 9 J 2y 1 35 M 28. 5x8 2y 10 (3x 1 18)8 29. E F (5x 2 6)8 y 1 3 2y 1 1 (4x 1 7)8 H G 30. HO EONE he diagonals of a rhombus are 6 inches and 8 inches. What is the perimeter of the rhombus? Explain. 31. MULILE HOIE ectangle is similar to rectangle FGHJ. If 5 5, 5 4, and FM 5 5, what is HJ? E F J M G H HOMU he diagonals of rhombus intersect at E. Given that m and E 5 8, find the indicated measure. 32. m 33. m E 34. m E 37. ENGLE he diagonals of rectangle Q intersect at. Given that m and Q 5 10, find the indicated measure. 38. m 39. m Q 40. Q Q 43. QUE he diagonals of square LMN intersect at K. Given that LK 5 1, find the indicated measure. 44. m MKN 45. m LMK 46. m LK 47. KN 48. M 49. L OOINE GEOMEY Use the given vertices to graph ~JKLM. lassify ~JKLM and explain your reasoning. hen find the perimeter of ~JKLM. 50. J(24, 2), K(0, 3), L(1, 21), M(23, 22) 51. J(22, 7), K(7, 2), L(22, 23), M(211, 2) L E K M N WOKE-OU OLUION on p. W1 5 NIZE E IE

8 62. EXENE EONE In, } i }, and } bisects. a. how that >. What can you conclude about and? What can you conclude about } and }? Explain. b. uppose you also know that } > }. lassify. Explain. 63. OVING HEOEM 8.13 Write a coordinate proof of the following statement, which is part of heorem If a quadrilateral is a rectangle, then its diagonals are congruent. 64. HLLENGE Write a coordinate proof of part of heorem GIVEN c FGH is a parallelogram, } G > } HF y (a,?) OVE c FGH is a rectangle. lan for roof Write the coordinates of the vertices in terms of a and b. Find and compare the slopes of the sides. H(?,?) G(?,?) O F(b, 0) x MIXE EVIEW EVIEW repare for Lesson 8.5 in Ex In njkl, KL centimeters. oint M is the midpoint of } JK and N is the midpoint of } JL. Find MN. (p. 295) Find the sine and cosine of the indicated angle. Write each answer as a fraction and a decimal. (p. 473) Find the value of x. (p. 507) x x x8 628 QUIZ for Lessons For what value of x is the quadrilateral a parallelogram? (p. 522) 1. 5x 1 3 7x (3x 2 13)8 3. 3x (x 1 19)8 5x 2 48 lassify the quadrilateral. Explain your reasoning. (p. 533) x 2x 2x x 540 EX IE for Lesson 8.4, p. 911 ONLINE QUIZ at classzone.com

### (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 =

### Recognize and apply properties of rectangles. Determine whether parallelograms are rectangles. are rectangles used in tennis?

ectangles Vocabulary rectangle ecognize and apply properties of rectangles. etermine whether parallelograms are rectangles. are rectangles used in tennis? any sports are played on fields marked by parallel

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,

### 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.

### 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

### 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

### 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

### 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

### Similar Polygons. Copy both triangles onto tracing paper. Measure and record the sides of each triangle. Cut out both triangles.

-7 Similar Polygons MAIN IDEA Identify similar polygons and find missing measures of similar polygons. New Vocabulary polygon similar corresponding parts congruent scale factor Math Online glencoe.com

### 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

### 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

### ch 8 review Name: Class: Date:

Name: Class: Date: ID: A ch 8 review 1. How many triangles are formed by drawing diagonals from one vertex in the figure? Find the sum of the measures of the angles in the figure. a. 5, 900 b. 5, 1080

### 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,

### 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

### To use properties of perpendicular bisectors and angle bisectors

5-2 erpendicular and ngle isectors ommon ore tate tandards G-O..9 rove theorems about lines and angles... points on a perpendicular bisector of a line segment are exactly those equidistant from the segment

### CHAPTER 7. Think & Discuss (p. 393) m Z 55 35 180. m Z 90 180. m Z 90 QR 2 RP 2 PQ 2 QR 2 10 2 12.2 2 QR 2 100 148.84 QR 2 48.84 AB 1 6 2 3 4 2 QR 7.

HPTER 7 Think & Discuss (p. 393). The image in bo is flipped to get the image in bo. The image in bo is turned to get the image in bo D.. Sample answer: If ou look at the picture as a whole, the right

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,

### Name Period 11/2 11/13

Name Period 11/2 11/13 Vocabulary erms: ongruent orresponding Parts ongruency statement Included angle Included side GOMY UNI 6 ONGUN INGL HL Non-included side Hypotenuse Leg 11/5 and 11/12 eview 11/6,,

### 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,

### 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

### 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

### Geometry Review (1 st semester)

NAME HOUR Geometry Review (1 st semester) 1) The midpoint of XY is Z. If XY = n and XZ = n + 15, what is YZ? A) 18 B) 6 C) 45 D) 90 ) What is RS? A) 5 B) 56 C) D) 70 ) Which is an obtuse angle? A) PQR

### 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

### 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?

### The height of a trapezoid is the. EXAMPLE Real-World Connection

0-. lan Objectives To find the area of a trapezoid To find the area of a rhombus or a kite Examples eal-world onnection Finding rea Using a Triangle Finding the rea of a Kite 4 Finding the rea of a hombus

### CONGRUENCE BASED ON TRIANGLES

HTR 174 5 HTR TL O ONTNTS 5-1 Line Segments ssociated with Triangles 5-2 Using ongruent Triangles to rove Line Segments ongruent and ngles ongruent 5-3 Isosceles and quilateral Triangles 5-4 Using Two

### 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. 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.

### 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

### 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

### 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

### 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

### 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.

### 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

### 4-1 Classifying Triangles. ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240.

ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240. Classify each triangle as acute, equiangular, obtuse, or right. Explain your reasoning.

### 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

### Classify each triangle as acute, equiangular, obtuse, or right. Explain your reasoning.

ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240. One angle of the triangle measures 90, so it is a right angle. Since the triangle has a

### 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 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

### 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

### 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.

### Seattle Public Schools KEY to Review Questions for the Washington State Geometry End of Course Exam

Seattle Public Schools KEY to Review Questions for the Washington State Geometry End of ourse Exam 1) Which term best defines the type of reasoning used below? bdul broke out in hives the last four times

### Perimeter and Area of Similar Figures

11.3 erimeter and Area of Similar igures Before You used ratios to find perimeters of similar figures. Now You will use ratios to find areas of similar figures. Why So you can apply similarity in cooking,

### 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

### Tangents to Circles. Circle The set of all points in a plane that are equidistant from a given point, called the center of the circle

10.1 Tangents to ircles Goals p Identify segments and lines related to circles. p Use properties of a tangent to a circle. VOULRY ircle The set of all points in a plane that are equidistant from a given

### 7.4 Showing Triangles are

age 1 of 7 7. howing riangles are imilar: and oal how that two triangles are similar using the and imilarity heorems. ey ords similar polygons p. he triangles in the avajo rug look similar. o show that

1 lassifying Quadrilaterals Identify and sort quadrilaterals. 1. Which of these are parallelograms?,, quadrilateral is a closed shape with 4 straight sides. trapezoid has exactly 1 pair of parallel sides.

### 1.7 Find Perimeter, Circumference,

.7 Find Perimeter, Circumference, and rea Goal p Find dimensions of polygons. Your Notes FORMULS FOR PERIMETER P, RE, ND CIRCUMFERENCE C Square Rectangle side length s length l and width w P 5 P 5 s 5

### 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,

### 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

### Geometry, Final Review Packet

Name: Geometry, Final Review Packet I. Vocabulary match each word on the left to its definition on the right. Word Letter Definition Acute angle A. Meeting at a point Angle bisector B. An angle with a

### 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

### 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,

### **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:

### NAME DATE PERIOD. Study Guide and Intervention

opyright Glencoe/McGraw-Hill, a division of he McGraw-Hill ompanies, Inc. 5-1 M IO tudy Guide and Intervention isectors, Medians, and ltitudes erpendicular isectors and ngle isectors perpendicular bisector

### Statements Goals Identify and evaluate conditional statements. Identify converses and biconditionals. Drafting, Sports, Geography

3-6 Conditional Statements Goals Identify and evaluate conditional statements. Identify converses and biconditionals. Applications Drafting, Sports, Geography Do you think each statement is true or false?

### 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

### /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

### 1.1. 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

### 2.6 Properties of Equality

age of 7 2.6 roperties of Equality and Goal Use properties of equality and congruence. Reflexive roperty Symmetric roperty Key Words Reflexive roperty Symmetric roperty Transitive roperty Jean is the same

### Parallel and Perpendicular. We show a small box in one of the angles to show that the lines are perpendicular.

CONDENSED L E S S O N. Parallel and Perpendicular In this lesson you will learn the meaning of parallel and perpendicular discover how the slopes of parallel and perpendicular lines are related use slopes

### 6.1. Perpendicular and Angle Bisectors

6.1 T TI KOW KI.2..5..6. TI TOO To be proficient in math, you need to visualize the results of varying assumptions, explore consequences, and compare predictions with data. erpendicular and ngle isectors

### 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.

### Ch 3 Worksheets S15 KEY LEVEL 2 Name 3.1 Duplicating Segments and Angles [and Triangles]

h 3 Worksheets S15 KEY LEVEL 2 Name 3.1 Duplicating Segments and ngles [and Triangles] Warm up: Directions: Draw the following as accurately as possible. Pay attention to any problems you may be having.

### 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 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

### Circle Name: Radius: Diameter: Chord: Secant:

12.1: Tangent Lines Congruent Circles: circles that have the same radius length Diagram of Examples Center of Circle: Circle Name: Radius: Diameter: Chord: Secant: Tangent to A Circle: a line in the plane

### 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

### Chapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?

Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane

### A segment that joins two nonconsecutive vertices of a polygon is called a diagonal. Polygon PQRST has two diagonals from vertex R, RP &* and RT&*.

age of 6 6. olygons Goal Identify and classify polygons. Find angle measures of quadrilaterals. Each traffic sign below is an example of a polygon. Notice that each sign is formed with straight lines.

### 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

### 5-1 Perpendicular and Angle Bisectors

5-1 Perpendicular and Angle Bisectors Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Construct each of the following. 1. A perpendicular bisector. 2. An angle bisector. 3. Find the midpoint and

### 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

### 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

### Geometry EOC Practice Test #2

Class: Date: Geometry EOC Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Rebecca is loading medical supply boxes into a crate. Each supply

### Quadrilateral Geometry. Varignon s Theorem I. Proof 10/21/2011 S C. MA 341 Topics in Geometry Lecture 19

Quadrilateral Geometry MA 341 Topics in Geometry Lecture 19 Varignon s Theorem I The quadrilateral formed by joining the midpoints of consecutive sides of any quadrilateral is a parallelogram. PQRS is

### Properties of Circles

10 10.1 roperties of ircles Use roperties of Tangents 10.2 ind rc Measures 10.3 pply roperties of hords 10.4 Use Inscribed ngles and olygons 10.5 pply Other ngle elationships in ircles 10.6 ind egment

### RATIO, PROPORTION, AND SIMILARITY

HPTER 474 12 HPTER TLE OF ONTENTS 12-1 Ratio and Proportion 12-2 Proportions Involving Line Segments 12-3 Similar Polygons 12-4 Proving Triangles Similar 12-5 ilations 12-6 Proportional Relations mong

### *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review

### 11-2 Areas of Trapezoids, Rhombi, and Kites. Find the area of each trapezoid, rhombus, or kite. 1. SOLUTION: 2. SOLUTION: 3.

Find the area of each trapezoid, rhombus, or kite. 1. 2. 3. esolutions Manual - Powered by Cognero Page 1 4. OPEN ENDED Suki is doing fashion design at 4-H Club. Her first project is to make a simple A-line

### 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

### Coordinate Graphing and Geometric Constructions

HPTER 9 oordinate Graphing and Geometric onstructions hapter Vocabular coordinate plane origin graph image line of reflection rotation midpoint -ais ordered pair quadrants translation line smmetr rotational

### (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

### 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:

### 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

### Geometry Chapter 5 Review Relationships Within Triangles. 1. A midsegment of a triangle is a segment that connects the of two sides.

Geometry Chapter 5 Review Relationships Within Triangles Name: SECTION 5.1: Midsegments of Triangles 1. A midsegment of a triangle is a segment that connects the of two sides. A midsegment is to the third

### 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

### Neutral Geometry. April 18, 2013

Neutral Geometry pril 18, 2013 1 Geometry without parallel axiom Let l, m be two distinct lines cut by a third line t at point on l and point Q on m. Let be a point on l and a point on m such that, are

### 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.

### 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

### Activity 4. Perimeters, Areas, and Slopes Oh, My! Objectives. Introduction. Problem. Exploration

Activity 4 Objectives Use analytic geometry to investigate the attributes of geometric figures Practice mathematical verification Use the Shading and Point-of-Intersection Trace features of the Inequality

### Solution: 2. Sketch the graph of 2 given the vectors and shown below.

7.4 Vectors, Operations, and the Dot Product Quantities such as area, volume, length, temperature, and speed have magnitude only and can be completely characterized by a single real number with a unit

### Pythagorean Theorem: 9. x 2 2

Geometry Chapter 8 - Right Triangles.7 Notes on Right s Given: any 3 sides of a Prove: the is acute, obtuse, or right (hint: use the converse of Pythagorean Theorem) If the (longest side) 2 > (side) 2

### Trade of Metal Fabrication. Module 5: Pipe Fabrication Unit 9: Segmental Bends Phase 2

Trade of Metal Fabrication Module 5: Pipe Fabrication Unit 9: Segmental Bends Phase 2 Table of Contents List of Figures... 5 List of Tables... 5 Document Release History... 6 Module 5 Pipe Fabrication...

### 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

### Coordinate 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 two-dimensional coordinate systems to

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

### Equation of a Line. Chapter H2. The Gradient of a Line. m AB = Exercise H2 1

Chapter H2 Equation of a Line The Gradient of a Line The gradient of a line is simpl a measure of how steep the line is. It is defined as follows :- gradient = vertical horizontal horizontal A B vertical