Question

if m∠fhg = m∠fhi = 60° and fi = 3, what is fg? fg = □

Explanation:

Step1: Identify congruent triangles

Since $\angle FHG=\angle FHI = 60^{\circ}$, $\angle I=\angle G = 90^{\circ}$ and $FH$ is common, $\triangle FHI\cong\triangle FHG$ (by the Angle - Angle - Side congruence criterion as $\angle I=\angle G$, $\angle FHI=\angle FHG$ and $FH = FH$).

Step2: Use congruent - side property

For congruent triangles $\triangle FHI$ and $\triangle FHG$, corresponding sides are equal. Given $FI = 3$, then $FG=FI$. So $FG = 3$.

Answer:

3