Question

Patricia uses the given isosceles triangle ABC to prove that the base angles of an isosceles triangle are congruent. The statements associated with the proof are listed below. Given: AB ? AC, AD ? BC Prove: ?B ? ?C Proof: Statements 1. AB ? AC, AD ? BC 2. m?ADB = m?ADC = 90° 3. AD ? AD 4. ?ADB ? ?ADC 5. ?B ? ?C Which of these reasons does NOT justify any of the statements given above? A. SAS postulate of congruence B. reflexive property C. definition of perpendicular lines D. CPCTC

          Patricia uses the given isosceles triangle ABC to prove that the base angles of an isosceles triangle are congruent. The statements associated with the proof are listed below.

Given: AB ? AC, AD ? BC

Prove: ?B ? ?C

Proof:
Statements
1. AB ? AC, AD ? BC
2. m?ADB = m?ADC = 90°
3. AD ? AD
4. ?ADB ? ?ADC
5. ?B ? ?C

Which of these reasons does NOT justify any of the statements given above?

A. SAS postulate of congruence
B. reflexive property
C. definition of perpendicular lines
D. CPCTC

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Patricia uses the given isosceles triangle ABC to prove that the base angles of an isosceles triangle are congruent. The statements associated with the proof are listed below.

Given: AB ? AC, AD ? BC

Prove: ?B ? ?C

Proof:
Statements
1. AB ? AC, AD ? BC
2. m?ADB = m?ADC = 90°
3. AD ? AD
4. ?ADB ? ?ADC
5. ?B ? ?C

Which of these reasons does NOT justify any of the statements given above?

A. SAS postulate of congruence
B. reflexive property
C. definition of perpendicular lines
D. CPCTC

Added by Megan R.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

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Solved by Expert Allison Knapp

03/03/2022

Step 1

We are given that triangle ABC is an isosceles triangle with AB = AC, and we need to prove that the base angles of an isosceles triangle are congruent. The base angles are ∠BAC and ∠DAC. Show more…

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Patricia uses the given isosceles triangle ABC to prove that the base angles of an isosceles triangle are congruent. The statements associated with the proof are listed below. Given: AB = AC, AD Proof: Statement 1: AB = AC; AD Reason: Reflexive property Statement 2: ""BAD = ""BAC Reason: Definition of congruent angles Statement 3: ""BAD = ""DAC Reason: Given Statement 4: ""BAC = ""DAC Reason: Transitive property Statement 5: ""BAC = ""DAC = ""BAD Reason: Transitive property Statement 6: ""BAC "‰… ""DAC Reason: Definition of congruent angles Therefore, the base angles of an isosceles triangle are congruent.

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