Question

Prove : $\overline{BA}=\overline{EF}$. By which postulate will you prove $\Delta ABC\cong \Delta EFC$

• A. SSS congruence criterion
• B. AAA congruence criterion
• C. ASA congruence criterion
• D. SAS congruence criterion

Answer 1

The correct option is D SAS congruence criterion

Given: 1) Point C is the midpoint of BF

2) $\overline{AC}=\overline{CE}$
In $\Delta ABC$ and $\Delta EFC$
$\overline{AC}=\overline{CE}$ (given)
$\angle ACB=\angle ECF$ (vertical angles are congruent)
$\overline{BC}=\overline{CF}$ (midpoint bisects segment into congruent parts)
$\Delta ABC\cong \Delta EFC$
$\overline{BA}=\overline{EF}$ (CPCT)
Therefore, D is the correct answer.