Question

1 pts

Given: C is midpoint of BD
AB 1 BD
BD I DE
Prove: AABC = AEDC
What will be the final reason" in this proof?
AAS
ASA
OSAS
H-L

Answer 1

ASA

Explanation:

Given:

Two triangles ABC and EDC such that:

AB ⊥ BD and BD ⊥ DE

C is the midpoint of BD.

The two triangles are drawn below.

Since, AB ⊥ BD and BD ⊥ DE

Therefore, the two triangles are right angled triangle. The triangle ABC is right angled at vertex B. The triangle EDC is right angled at vertex D.

Since, point C is the midpoint of the line segment BD.

Therefore, C divides the line segment BD into two equal parts.

So, segment BC ≅ segment CD (Midpoint theorem)

Now, consider the triangles ABC and EDC.

Statements Reason

1. ∠ABC ≅ ∠CDE Right angles are congruent to each other

2. BC ≅ CD Midpoint theorem. C is midpoint of BD

3. ∠ACB ≅ ∠ECD Vertically opposite angles are congruent

Therefore, the two triangles are congruent by ASA postulate.

So, the second option is correct.