Question

Consider triangle ABC and triangle ACD in the diagram below. Which of the following complete the proof above?

Options
- AB =AD
- AC=AC
- AC=BD
- BC=DC

Answer 1

BC=DC

Explanation:

I did the test yourself and got it right :)

Answer 2

Given:

AC is perpendicular bisector of BD

AB ≅ AD

To prove:

ΔABC ≅ ΔACD

Solution:

In triangle ABC and triangle ACD,

Step 1: Given

AC is perpendicular bisector of BD and

AB ≅ AD (Side)

Step 2: By perpendicular bisector definition,

BC ≅ CD (Side)

Step 3: By reflexive property,

AC ≅ AC (Side)

Step 4: By SSS congruence criterion,

ΔABC ≅ ΔACD

Hence proved.