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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
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
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Write the additional corresponding parts of the given pairs of triangles that must be congruent to apply the indicate postulate theorem.
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: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.
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
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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