Resource Master 75 Lesson 5 3

Table of Justifications

CSÖmejustifications that

segments are congruent

Definition of bisector:

If a figure is the bisector of a segment, it

divides the segment into two congruent

segments. (Lesson 3-9)

Definition of midpoint:If a point is the midpoint of a segment, it

divides the segment into two congruent

segments. (Lesson 2-4)

CPCF Theorem:

If figures are congruent, then

corresponding segments are congruent.

(Lesson 5-2)

Segment Congruence Theorem:

If segments have equal measures, then the

segments are congruent. (Lesson 5-2)

Definition of circle:

If a figure is a circle, then its radii are

congruent. (Lesson 2-4)

Definition of congruence:

If a segment is the image of another under

an isometry, then the segment and its

image are congruent. (Lesson 5-1)

Some justifications that.

angles are congruent

Corresponding Angles Postulate:

If lines intersected by a transversal are

parallel, then corresponding angles are

congruent (Lesson 3-6)

Definition of angle bisector:

If a ray bisects an angle, then it divides

the angle into two congruent angles.

(Lesson 3-3)

CPCF Theorem:

If figures are congruent, then

corresponding angles are congruent.

(Lesson 5-2)

Angle Congruence Theorem:If the measures of angles are equal, then

the angles are congruent. (Lesson 5-2)

Vertical Angles Theorem:If angles are vertical angles, then they are

congruent. (Lesson 3-3)

Definition of congruence:If an angle is the image of another under

an isometry, then the angle and its image

are congruent. (Lesson 5-1)

0)

0

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Lesson Master

PROPERTIES Objective F

Answer Page

Questions on SPUR ObjectivesSee Student Edition pages 302—305 for objectives.

In 1—5, use one of the justifications at the right for each conclusion,1. If M is the midpoint of PQ, then QM.

2. IfAB bisects ZTAR, then ZTAB ZBAR.

3. If PQRS - rm(ABCD), then PQRS ABCD.

4. If PQRS ABCD, then QR BC.

5. If QR BC, then QR = BC.

CPCFTheorem

Definition of congruence

Definition of midpoint

Definition of circle

Definition of angle bisector

Vertical Angles Theorem

Segment Congruence Theorem

Angle Congruence Theorem

n 6—8, use the figure at the right. AB and CD are diameters ofGive a justification for the conclusion. You may use the justificationsfrom the box above.

6. öÄæäD cc CT7. Z-AOD=ZCOB

8. ZCOA ZBOD

In 9 and 10, use the figure at the right and the CorrespondingAngles Postulate.

Corresponding Angles Postulate:Suppose two coplanar lines are cut by a transversal.

a. If two corresponding angles have the same measure,then the lines are parallel.

D

12

5678

c

n

b. If the lines are parallel, then corresponding angleshave the same measure.

9. If you know that m Il n, which part of the Corresponding AnglesPostulate lets you conclude that Z3 Z7?

10. If you know that Z2 Z6, which part of the Corresponding AnglesPostulate lets you conclude that m Il n?

230 Geometry

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Name

Lesson Master

PROPERTIES Objective F

Answer Page

Questions on SPUR ObjectivesSee Student Edition pages 302—305 for objectives.

Multiple Choice In 1-5, choose the justification which allows you to makethe given conclusion.

1. IfEFGHæABCD, then EF=AB.

A Segment Congruence fieorem B Definition of midpoint

C CPCFTheorem D Definition of congruence

2. If Z-X= LA, then mZX = mZA.

A Angle Congruence Theorem B Definition of angle bisector

C Angle Measure Postulate D Corresponding Angles Postulate

3. If H is the midpoint of DU, then DH HU

A Segment Congruence Theorem B Definition of midpoint

C CPCFTheorem D Definition of congruence

4. Ifr (ARDO) = LYTM, then ARDO = LEM.

A Definition of congruence B Reflexive Property of Congruence

C CPCF'1heorem D Definition of reflection

5. If Z4 and Z7 are vertical angles, then Z4 Z7

A Definition of vertical angles B Vertical Angles Theorem

C Angle Congruence %eorem D Definition of congruence

o

Geometry 231

Answer Page

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page 25-3B

In 6-11, r b-G(AOMU) = AOMD. Provide a justification for the conclusion.

6. AOMU AOMD

7. 0M is the perpendicular bisector of UI).

8.

9.

10.

11. Qfo

12. In the diagram at the right, A, B, and C are on @O, and 0Bbisects LAOC. List three conclusions you can deduce andjustify the conclusion. c

o

a. ( 13 COB

b. oft = oc Dec. oc c.

c.Z DOC=ZAOC

13. Write a proof.

Given Z3 L8Prove m Il n 43

12 m

56 n7

Cc

VI

232 Geometry