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