Question

Please help with this question; I need to prove to my parents I am not as much of a disappointment to them as they think I am.

Answer 1

Triangles ABD and CBD are congruent by SAS.

Explanation:

Sides AD and CD are congruent since they both measure 15.

Angles ADB and CDB are congruent because of the angle bisector.

Side DB is congruent to itself.

By SAS, triangles ABD and CBD are congruent.

Answer: Triangles ABD and CBD are congruent by SAS.

Answer 2

ΔABD ≅ ΔCBD by SAS Congruence Postulate (Option C)

Explanation:

In ΔABD & ΔCBD ,

1) AD = CD = 15 units

2) ∠ADB = ∠CDB (∵ BD is angle bisector)

3) BD = BD (common side)

∴ ΔABD ≅ ΔCBD by SAS congruence postulate.