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Given: FH ⊥ GH; KJ ⊥ GJ

Prove: ΔFHG ~ ΔKJG

Triangles F H G and K J G connect at point G. Angles F H G and K J G are right angles.

Identify the steps that complete the proof.

♣ =

♦ =
♠ =

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Martebi

The fill up for the missing steps are:

  • all right angles are congruent.
  • angle FGH is congruent to angle KGJ.
  • AA similarity theorem.

When is an angle known to be congruent?

Note that we are given:

  • FH ⊥ GH
  • KJ ⊥ GJ

Based on the definition of perpendicular lines, ΔFHG ~ ΔKJG  are known to be right angles.

So: Δ FHG ≅  ΔKJG due to the fact that all the right angles are congruent.

ΔFHG  and  ΔKGJ are vertical angles and as such, the angle are congruent to angle  ΔKGJ

Based on AA similarity theorem, ΔFHG ~ ΔKJG

Due to the above, the fill up for the missing steps are:

  • all right angles are congruent.
  • angle FGH is congruent to angle KGJ.
  • AA similarity theorem.

Learn more about congruent angles from

https://brainly.com/question/7724930

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