Question

I need help on a problem

Answer 1

Here, from the figure we see that,

Line EI is parallel to HG.

And EH and GI act as the transversal lines for the given parallel pair.

So, we get

$\begin{gathered} \angle G=\angle I\text{ (alternate angles)} \\ \angle E=\angle H\text{ (alternate angles)} \\ \angle EFI=\angle GFH(vertically\text{ opposite angles)} \end{gathered}$$\text{Also in }\Delta EIF\text{ side }FI\text{ is given equal to side }FG\text{ in }\Delta FGH$

Therefore, we have two angles and one side equal in two triangles.

Henceproved that , they are congruent with the ASA (Angle Side Angle)rule.