Question

Given start overline, B, D, end overline

BD
bisects start overline, A, C, end overline
AC
, complete the flowchart proof below. Note that the last statement and reason have both been filled in for you.

Answer 1

Explanation:

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Answer 2

The completed flowchart proof:

Given: BD bisects AC

Statement | Reason

1. BD bisects AC | Given

2. AB = BC | Definition of angle bisector

3. ∠ABD = ∠CBD | Vertical angles are congruent

4. BD = BD | Reflexive property of congruence

5. ΔABD ≅ ΔCBD | SAS (Side-Angle-Side)

Given that (BD) bisects (AC), we can use the SAS (side-angle-side) congruence theorem to prove that ΔABD ≅ ΔCBD. The flowchart proof is as follows:

This is given in the problem statement.

Since BD is perpendicular to AC , the two angles formed are vertical angles, which are always congruent.

The reflexive property of congruence states that any segment is congruent to itself.

We have shown that two sides (BD) and two angles (ABD and CBD) are congruent in the two triangles. Therefore, by the SAS (Side-Angle-Side) postulate, the two triangles are congruent.