32
QuizMultiple Choice

N/A — Exam

Question 32 • Geometry

What is the missing reason in the proof? Statements Reasons 1. line segment AB is parallel to line segment CD ; line segment BC is parallel to line segment DA 1. given 2. Quadrilateral ABCD is a parallelogram 2. definition of parallelogram 3. line segment AB is congruent to line segment CD ; line segment BC is congruent to line segment DA 3. opposite sides of a parrallegram are is congruent to 4. line segment AC is congruent to line segment AC 4. refexive property 5. triangle ABC is congruent to triangle CDA 5. ?

Answer
A
SSS congruence theorem
B
HL theorem
C
Pythagorean theorem
D
perpendicular bisector theorem

Explanation

The triangles have three pairs of congruent sides: AB ≅ CD and BC ≅ DA because opposite sides of a parallelogram are congruent, and AC ≅ AC by the reflexive property. Therefore, △ABC ≅ △CDA by the SSS congruence theorem. The correct choice is A, SSS congruence theorem.

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