Question

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

Answer 1

Since BD is the angle bisector of ∠ ABC,

∠ ABD = ∠ CBD --- (1)

Now, in triangles Δ ABD and Δ CBD,

BD = BD (common side)

∠ ABD = ∠ CBD from (1)

AB = BC (Given)

Hence, Δ ABD ≅ Δ CBD (SAS Rule).