Question

Write a 2-column proof with an statement & reason column

Answer 1

Given that,

AB is congruent to CB

BD is a median of AC

To prove: Triangle ABD and Triangle CBD are congruent.

Proof:

From given we get that,

`AB\cong CB`

Also, we have BD is a median of AC.

BD cuts the side AC into two equal parts.

D is the midpoint of AC.

we get,

`AD=CD`

Also BD is the common side for both triangles ABD and CBD

From the definition:

SSS Congruence rule: If three sides of one triangle are equal to the corresponding sides of another triangle, then the triangles are congruent.

Using SSS Congruence rule, we get that,

`\Delta ABD\cong\Delta CBD`

Hence proved.