Question

3. Segment GE is an angle bisector of both

Answer 1

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:

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