Chapter Test
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Can you identify any congruent angles using the parallel sides?
See solution
Examining the diagram, we see that MK is shared by the triangles. Therefore, by the Reflexive Property of Congruence, we know this side is congruent.
Let's add all the new information we have about the triangles to our diagram.
Since two angles and the included side of △ MJK are congruent to two angles and the included side of △ KLM, we can prove congruence by the ASA Congruence Theorem.
Statement
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Reason
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1. JK ∥ ML, MJ ∥ KL
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1. Given
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2. MK ≅ MK
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2. Reflexive Property of Congruence
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3. ∠ JMK ≅ ∠ LKM, ∠ JKM ≅ ∠ LMK
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3. Alternate Interior Angles Theorem
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4. △ MJK ≅ △ KLM
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4. ASA Congruence Theorem
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