Question

Given: `Delta` ABC is an isosceles triangle where AB = BC Prove: `"m"/_BAC = "m"/_BCA` Statement Reason 1. Let `DeltaABC` be an isosceles triangle where AB = BC. given 2. Create point D on side `bar(AC)` so that `bar(BD)` bisects `/_ABC` as shown. constructing an angle bisector 3. `"m"/_ABD = "m"/_CBD` 4. BD = BD Reflexive Property of Equality 5. `DeltaABD ~= DeltaCBD` SAS 6. `"m"/_BAC = "m"/_BCA` Corresponding angles of congruent triangles have equal measures. What is the reason for statement 3 in this proof? A. definition of angle bisector B. Alternate Interior Angles Theorem C. Corresponding Angles Theorem D. Corresponding angles of congruent triangles are congruent.

Answer 1

The answer is NOT D. Corresponding angles of congruent triangles are congruent

Answer 2

Thank you for asking this question. Here is your answer:

BD is the angle bisector of ∠ABC

∠ ABD = ∠ CBD --- (equation 1)

In triangles Δ ABD and Δ CBD

BD = BD (this is the common side)

∠ ABD = ∠ CBD

AB = BC (this is given)

Δ ABD ≅ Δ CBD (this is the SAS Rule)

If there is any confusion please leave a comment below.