danielarodriguezz080
Answered

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3. Segment GE is an angle bisector of both
angle HEF and angle FGH. Prove triangle HGE is
congruent to triangle FGE.
F
H
G

3 Segment GE Is An Angle Bisector Of Both Angle HEF And Angle FGH Prove Triangle HGE Is Congruent To Triangle FGE F H G class=

Sagot :

akposevictor

ΔHGE and ΔFGE are congruent by the Angle-Side-Angle Congruence Theorem (ASA).

Recall:

  • A segment that divides an angle into equal parts is known as an angle bisector.
  • Two triangles are congruent by the ASA Congruence Theorem if they share a common side and have two pairs of congruent angles.

In the diagram given, Angle bisector, GE, divides ∠HEF into congruent angles,  ∠HEG ≅ ∠GEF.

Also divides ∠FGH into congruent angles, ∠HGE ≅ ∠FGE.

Both triangles also share a common side, GE

This implies that: ΔHGE and ΔFGE have:

two pairs of congruent angles - ∠HEG ≅ ∠GEF and ∠HGE ≅ ∠FGE

a shared side - GE

Therefore, ΔHGE and ΔFGE are congruent by the Angle-Side-Angle Congruence Theorem (ASA).

Learn more about ASA Congruence Theorem on:

https://brainly.com/question/82493

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