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Chapter 5

Resource Masters

Geometry

Consumable Workbooks

Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks. Study Guide and Intervention Workbook0-07-860191-6

Skills Practice Workbook0-07-860192-4

Practice Workbook0-07-860193-2

Reading to Learn Mathematics Workbook0-07-861061-3 ANSWERS FOR WORKBOOKSThe answers for Chapter 5 of these workbooks can be found in the back of this Chapter Resource Masters booklet. Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with GlencoeÕs Geometry.Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.

Send all inquiries to:

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8787 Orion Place

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ISBN: 0-07-860182-7

Geometry

Chapter 5 Resource Masters

1 2 3 4 5 6 7 8 9 10 009 11 10 09 08 07 06 05 04 03

Chapter 5 Test, Form 155

©Glencoe/McGraw-Hill275Glencoe Geometry

Assessments

Write the letter for the correct answer in the blank at the right of each question. For Questions 1Ð4, use the figure at the right. 1.

Name an altitude.

A.DEB.AB

C.GB D.CF

2.Name a perpendicular bisector.

A.DEB.ABC.GB

D.CF

3.Name an angle bisector.

A.DEB.ABC.GB

D.CF

4.Name a median.

A.DEB.ABC.GB

D.CF

For Questions 5Ð7, use the figure to determine

which is a true statement for the given information. 5.

ACis a median.

A.mACD90B.BACDAC

C.BCCDD.BD

6.ACis an angle bisector.

A.mACD90B.BACDACC.BCCDD.BD

7.ACis an altitude.

A.mACD90B.BACDACC.BCCDD.BD

8.Name the longest side of DEF.

A.DEB.EF

C.DFD.cannot tell

9.Which angle in ABChas the greatest measure?

A.AB.B

C.CD.cannot tell

10.Given ABCwith vertices A(2, 6),B(4,2), and C(8,6), find an equation

for the line containing the altitude to AB. A.y 3 4 x 5 4 B.y 4 3 x 1 30
C.y 3 4 xD.y 8 9 x 1 90

11.Given ABCwith vertices A(2, 6),B(4,2), and C(8,6), find an equation

for the line containing the median to AB. A.y 3 4 x 5 4 B.y 4 3 x 1 30
C.y 3 4 xD.y 8 9 x 1 90
ACB 95
7 D

6210108

FE ADCB A B CDE FG 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

NAME DATE PERIOD

SCORE

Standardized Test Practice

Student Record Sheet(Use with pages 278Ð279 of the Student Edition.) 55

©Glencoe/McGraw-HillA1Glencoe Geometry

Answers

Select the best answer from the choices given and fill in the corresponding oval. 147
258
36

DCBADCBA

DCBADCBADCBA

DCBADCBADCBA

NAME DATE PERIOD Part 1Multiple ChoicePart 1Multiple ChoicePart 2Short Response/Grid InPart 2Short Response/Grid InPart 3Open-EndedPart 3Open-Ended

Solve the problem and write your answer in the blank. For Question 9, also enter your answer by writing each number or symbol in a box. Then fill in the corresponding oval for that number or symbol.

9(grid in)9

10 11 12

000...

99998765

4321876543218765432187654321

Record your answers for Questions 13Ð14 on the back of this paper.

©Glencoe/McGraw-HillA2Glencoe Geometry

Study Guide and InterventionBisectors, Medians, and Altitudes NAME ______________________________________________ DATE ____________ PERIOD _____

5-15-1

Glencoe/McGraw-Hill

245

Glencoe Geometry

Lesson 5-1

Perpendicular Bisectors and Angle Bisectors

A perpendicular bisectorof a

side of a triangle is a line, segment, or ray that is perpendicular to the side and passes through its midpoint. Another special segment, ray, or line is an angle bisector,which divides an angle into two congruent angles.

Two properties of perpendicular bisectors are:

(1) a point is on the perpendicular bisector of a segment if and only if it is equidistant from the endpoints of the segment, and (2) the three perpendicular bisectors of the sides of a triangle meet at a point, called the circumcenterof the triangle, that is equidistant from the three vertices of the triangle.

Two properties of angle bisectors are:

(1) a point is on the angle bisector of an angle if and only if it is equidistant from the sides of the angle, and (2) the three angle bisectors of a triangle meet at a point, called the incenterof the triangle, that is equidistant from the three sides of the triangle. BD is the perpendicular bisector of A C .Find x. BD is the perpendicular bisector of A C ,so ADDC.

3x8 5x6

14 2x 7 x 3 x 85
x 6 BC D A MR is the angle bisector of NMP.Find xif m1 5x8 and m2 8x16. MR is the angle bisector of NMP,so m1 m2.

5x8 8x16

24 3x
8 x 12 NR

PMExample

1

Example

1

Example

2

Example

2

ExercisesExercises

Find the value of each variable.

1. 2. 3.

DE is the perpendicular CDFis equilateral.DF bisects CDE. bisector of A C x 10; y 2 x 7.5 x 7

4.For what kinds of triangle(s) can the perpendicular bisector of a side also be an angle

bisector of the angle opposite the side? isosceles triangle, equilateral triangle

5.For what kind of triangle do the perpendicular bisectors intersect in a point outside the

triangle? obtuse triangle FE DC (4 x 30)8
x DF C E 10 y 46
x 3 x 8 y CED AB 7 x 96
x 2

Glencoe/McGraw-Hill

246

Glencoe Geometry

Medians and Altitudes

A medianis a line segment that connects the vertex of a triangle to the midpoint of the opposite side. The three medians of a triangle intersect at the centroidof the triangle. CentroidThe centroid of a triangle is located two thirds of the distance from a Theoremvertex to the midpoint of the side opposite the vertex on a median. AL 2 3

AE, BL

2 3

BF, CL

2 3 CD

Points R,S,and Tare the midpoints

of A B ,B C and A C ,respectively. Find x,y,and z. CU 2 3 CR BU 2 3 BT AU 2 3 AS 6x 2 3 (6x15) 24 2 3 (24 3y3) 6z4 2 3 (6z4 11)

9x6x15 3624 3y3

3 2 (6z4)6z4 11

3x15 3621 3y9z66z15

x5153y3z9 5yz3

Find the value of each variable.

1. x 4 2. x 6; y 5 B D is a median.ABCB;D,E,and Fare midpoints. 3. x 3; y 54.
x 12; y 5; z 2

EHFHHG

5. x 2; y 2; z 2 6. x 6; y 5; z 8 Vis the centroid of RST;Dis the centroid of ABC.TP18;MS15;RN24

7.For what kind of triangle are the medians and angle bisectors the same segments?

equilateral triangle

8.For what kind of triangle is the centroid outside the triangle?

not possible PM VT N RSy xz GF EB AC 24
32
9 z 6 6 z 6 x 8 y MJ PNO LK 3 y 5 2 x 6 z 1224

10HGFE

7 x 49
x 2 5 y DB EF AC 9 x 610
x 3 y 15 D BAC 6 x 37
x 1 ACTS RUB 3 y 36
x 1524
11 6 z 4 ACFE D

LBcentroid

Study Guide and Intervention

(continued)

Bisectors, Medians, and Altitudes

NAME ______________________________________________ DATE ____________ PERIOD _____

5-15-1

ExampleExample

ExercisesExercises

Answers(Lesson 5-1)

quotesdbs_dbs20.pdfusesText_26

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