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

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15-12-2017
Mathematics

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

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ahirohit963 ahirohit963 · Answer 1 · 2021-11-02T07:45:27+01:00

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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