ΔHGE and ΔFGE are congruent by the Angle-Side-Angle Congruence Theorem (ASA).
<em><u>Recall:</u></em>
- 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
<em>This implies that: ΔHGE and ΔFGE have:</em>
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:
brainly.com/question/82493
Answer:
=h+48
Step-by-step explanation:
59+h−11
=59+h+−11
Combine Like Terms:
=59+h+−11
=(h)+(59+−11)
Answer
=h+48
Hope I was helpful!!
Answer:
21
Step-by-step explanation:
Using alternate interior angles, we can conclude that angle C is equal to X (the 3rd, unmarked angle in the center triangle)
To find that 3rd angle, we can do 180 - 105 - 54. This is because all angles in a triangle must equal 180. Using this, we find that angle C is equal to 21. By the law, X must also equal 21.
