Question

Choose the missing reason in the proof.

A.) AAS
B.) ASA
C.) SSA
D.) SAS

Answer 1

D.) SAS

Explanation:

AB = AC

BD = CD

<B = <C

So 2 triangles are congruent by SAS

Answer 2

Answer: D.) SAS

Explanation:

SAS congruence postulate says that if two sides and the included angle of a triangle are congruent to corresponding two sides and the included angle of other triangle then we say the two triangles are congruent.

In the given proof , in ΔABD and ΔACD

`\overline{AB}\cong\overline{AC}` [side] (given)

`\overline{BD}\cong\overline{CD}` [side] (given)

`\angle{B}=\angle{C}` [included angle] (Base angles of isosceles triangles are congruent.)

So by SAS congruence postulate ΔABD ≅ ΔACD.