Upload
others
View
4
Download
0
Embed Size (px)
Citation preview
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
Back to Lesson 5-3
Name
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
Back to Lesson 5-3
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
Back to Lesson 5-3
Name
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