Q:

# Given: FH ⊥ GH; KJ ⊥ GJ Prove: ΔFHG ~ ΔKJG Identify the steps that complete the proof. ♣ = ♦ = ♠ =

Accepted Solution

A:
Right angles are congruent therefore, $$\rm \angle FHG \cong \angle GJK$$. $$\rm \angle FGH\;and \; \angle KGJ$$ are vertical angles hence they are also congruent to each other. And according to AA similarity theorem, two triangles are similar if there corresponding angles are congruent, therefore, $$\rm \Delta FHG \sim \Delta KJG$$.Given :$$\rm FH \perp GH$$$$\rm KJ \perp GJ$$According to the definition of perpendicular lines, $$\rm \angle FHG$$ and $$\rm \angle GJK$$ are the right angles.$$\rm \angle FHG \cong \angle GJK$$ because all right angles are congruent.$$\rm \angle FGH\;and \; \angle KGJ$$ are vertical angles therefore, angle $$\rm \angle FGH$$ are congruent to angle $$\rm \angle KGJ$$.According to AA similarity theorem, $$\rm \Delta FHG \sim \Delta KJG$$.Right angles are congruent therefore, $$\rm \angle FHG \cong \angle GJK$$. $$\rm \angle FGH\;and \; \angle KGJ$$ are vertical angles hence they are also congruent to each other. And according to AA similarity theorem, two triangles are congruent if there corresponding angles are congruent, therefore, $$\rm \Delta FHG \sim \Delta KJG$$.For more information, refer the link given below: