7
QuizMultiple Choice

Triangle Congruence — Test

Question 7 • Geometry

What is the missing reason in the proof? Statements Reasons 1. angle EGF is congruent to angle HGK 1. vert. angle cap s are is congruent to 2. line segment KH is parallel to line segment EF 2. given 3. angle cap f is congruent to angle cap k 3. alt. int. angle cap s are is congruent to 4. cap g is the midpoint of line segment KF 4. given 5. line segment FG is congruent to line segment KG 5. def. of midpt. 6. triangle FEG is congruent to triangle KHG 6. ? 7. line segment HG is congruent to line segment EG 7. CPCTC

Answer
A
SAS
B
HL
C
AAS
D
ASA

Explanation

The triangles have two pairs of congruent angles: ∠EGF ≅ ∠HGK by the vertical angles theorem, and the angles at F and K are congruent because the parallel lines create alternate interior angles. The included sides FG and KG are congruent because G is the midpoint of KF. Therefore, △FEG ≅ △KHG by ASA, choice D.

AI-written and checked against the verified answer.

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