Question

select the correct answer. you have this information about △abc, △fde, and △gih. ab = df ab = gi bc = hi de = hi m∠b = m∠d = m∠i which triangles must be congruent? a. △abc, △fde, and △gih b. △abc and △fde only c. △gih and △abc only d. none of the triangles

Explanation:

Step1: Recall congruence criteria

The Side - Angle - Side (SAS) congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the two triangles are congruent.

Step2: Analyze given information for $\triangle ABC$ and $\triangle FDE$

We know that $AB = DF$, $BC=DE$ (since $BC = HI$ and $DE = HI$) and $\angle B=\angle D$. By the SAS congruence criterion, $\triangle ABC\cong\triangle FDE$.

Step3: Analyze information for $\triangle ABC$ and $\triangle GIH$

We have $AB = GI$, $BC = HI$ and $\angle B=\angle I$. By the SAS congruence criterion, $\triangle ABC\cong\triangle GIH$.

Step4: Analyze information for $\triangle FDE$ and $\triangle GIH$

Since $\triangle ABC\cong\triangle FDE$ and $\triangle ABC\cong\triangle GIH$, then $\triangle FDE\cong\triangle GIH$ by the transitive property of congruence.

Answer:

A. $\triangle ABC$, $\triangle FDE$, and $\triangle GIH$