Question

these figures are congruent. what is hi?
□ miles

Explanation:

Step1: Find angle B in △BCD

First, calculate the missing angle in △BCD using the triangle angle sum theorem (sum of angles = 180°).
$\angle B = 180^\circ - 78^\circ - 40^\circ = 62^\circ$

Step2: Match congruent triangle parts

Identify the corresponding sides of the congruent triangles. In △BCD, side opposite $\angle B (62^\circ)$ is $DC$. In △HIJ, side opposite $\angle H (62^\circ)$ is $JI = 50$ mi. Wait, correct correspondence: △BCD ≅ △JIH (matching angles: $\angle B = \angle H = 62^\circ$, side $BC = JH = 56$ mi). So side $HI$ corresponds to side $BD$.

Step3: State the length of HI

Since congruent triangles have equal corresponding sides, $HI = BD = 36$ mi.

Answer:

36 miles