Question

Given: Base ∡BAC and ∡ACB are congruent.

Prove: ∆ABC is an isosceles triangle.

When completed, the following paragraph proves that line ab is congruent to line bc making ∆ABC an isosceles triangle.

Construct a perpendicular bisector from point B to line ac .
Label the point of intersection between this perpendicular bisector and line ac as point D.
m∡BDA and m∡BDC is 90° by the definition of a perpendicular bisector.
∡BDA is congruent to ∡BDC by the _______1________.
line ad is congruent line dc to by _______2________.
∆BAD is congruent to ∆BCD by the Angle-Side-Angle (ASA)

Answer 1

a. 1. the definition of congruent angles
2. Angle-Side-Angle (ASA) Postulate

b. 1. the definition of congruent angles
2. the definition of a perpendicular bisector

c. 1. Angle-Side-Angle (ASA) Postulate
2. the definition of a perpendicular bisector

d. 1. Angle-Side-Angle (ASA) Postulate
2. corresponding parts of congruent triangles are congruent (CPCTC)

Answer 2

i dont think it is A...
so that leaves me with B Cand D. any help? @SmoothMath

Answer 3

The CPCTC is the only part that looks correct to me. Since you're proving two triangles are congruent, and then showing one part of those triangles is congruent.

Answer 4

The correct answers are: 1) the two triangles are congruent by "side-angle-side" 2) AB is congruent to BC by "CORRESPONDING parts of congruent triangles are congruent (CPCTC)"

Answer 5

idk that really confusing but i think i might be right

Answer 6

Okay, thank you for your help(:

Answer 7

no problem...