Respuesta :
Right angles are congruent therefore, [tex]\rm \angle FHG \cong \angle GJK[/tex]. [tex]\rm \angle FGH\;and \; \angle KGJ[/tex] 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, [tex]\rm \Delta FHG \sim \Delta KJG[/tex].
Given :
- [tex]\rm FH \perp GH[/tex]
- [tex]\rm KJ \perp GJ[/tex]
According to the definition of perpendicular lines, [tex]\rm \angle FHG[/tex] and [tex]\rm \angle GJK[/tex] are the right angles.
- [tex]\rm \angle FHG \cong \angle GJK[/tex] because all right angles are congruent.
- [tex]\rm \angle FGH\;and \; \angle KGJ[/tex] are vertical angles therefore, angle [tex]\rm \angle FGH[/tex] are congruent to angle [tex]\rm \angle KGJ[/tex].
- According to AA similarity theorem, [tex]\rm \Delta FHG \sim \Delta KJG[/tex].
Right angles are congruent therefore, [tex]\rm \angle FHG \cong \angle GJK[/tex]. [tex]\rm \angle FGH\;and \; \angle KGJ[/tex] 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, [tex]\rm \Delta FHG \sim \Delta KJG[/tex].
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https://brainly.com/question/23790352
