Question

11 fill in the blank 10 points
11.
$\triangle efg cong \triangle \boxed{}$ by $\boxed{}$

Explanation:

Step1: Identify congruent parts

From the diagram: $\angle F = \angle H = 90^\circ$, $\angle E = \angle I$, $\angle EGF = \angle IGH$, and $FG = HG$ (implied by vertical angles and right triangles).

Step2: Match congruent triangle

The corresponding triangle to $\triangle EFG$ is $\triangle IHG$, as all matched angles and side correspond.

Step3: Determine congruence rule

We have two angles and a non-included side (AAS) congruent: $\angle F \cong \angle H$, $\angle E \cong \angle I$, $FG \cong HG$.

Answer:

$\triangle EFG \cong \triangle IHG$ by AAS (Angle-Angle-Side)