Giver CD a V E other Prove D Statements CD and OE bisect each other at pint V Cô = CÓ 1. 2. 3. Vertical A OV = EV A COV = A DEV CO = DE 4. 5. 6.
Giver CD a V E other Prove D Statements CD and OE bisect each other at pint V Cô = CÓ 1. 2. 3. Vertical A OV = EV A COV = A DEV CO = DE 4. 5. 6.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
Write the additional corresponding parts
of the given pairs of triangles that must be congruent to apply the indicate postulate theorem.

Transcribed Image Text:Illustrative Example 2
Given: AB = CB
BD bisects ZABC
D
Prove: AD CD
Statements
Reasons
1. AB = CB
2. BD bisects ZABC
3. ZABD E ZCBD
4. BD BD
5. AABD E ACBD
6. AD CD
1. Given
2. Given
3. Definition of angle bisector
4. Reflexivity
5. SAS Congruence Postulate
6. СРСТС
From the given illustrative example above, you proved that the two triangles
are congruent by SAS Congruence postulate. And because the parts of congruent
triangles are congruent (CPCTC), AD = CD.
Illustrative Example 3
L.
Given: LOVE is Rhombus
Prove: 2LOE ZVEO
E
Statement
Reasons
1.LOVE is a rhombus
2. LO . VE and LE = VO
3, OE E OE
4. ALOE = AVEO
5.
1. Given
2. Definition of rhombus
3. Reflexivity
4 SSS Congruence Postulate
5, CPCTC
ZLOE <VEO
In illustration example 3, ALOE E AVEO by SSS Congruence Postulate therefore ZLOE = ZVEO by
СРСТС.
Illustrative Example 4
A
P
Given: 2C and ZR are right angles
AB = PQ
ZB 2Q
R
Prove: ZA ZP
B
Statements
Reasons
1.2C and zR are right angles
2.2C ZR
1. Given
2. Any two right angles are
congruent
3. Given
4. Given
3. AB PQ
4. ZB 2Q
5. AABC APOR
6. ZA ZP
5. SAA Congruence Theorem
6. СРСТС
Since AABC and APQR are congruent by SAA Congruence Theorem,
then ZA = ZP by CPCTC.
Now, it is your turn to practice your skills in proving corresponding parts of congruent
triangles.

Transcribed Image Text:Activity 3
C
Given:
CD and OE bisect each
other at point V
V
E
Prove: CO = DE
Statements
Reasons
1. CD and OE bisect each other at
point V
2. CO = CO
3. 2 1 2
1.
2.
3. Vertical Angle Theorem
4. OV = EV
5. A COV =A DEV
4.
5.
6.
6. CÓ = DE
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