Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
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Exercise 2 Page 651

Can you identify any congruent angles using the parallel sides?

See solution

Practice makes perfect

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.

Also, if we consider MK as a transversal, we can find two pairs of alternate interior angles. Since JK ∥ ML and MJ ∥ KL we know by the Alternate Interior Angles Theorem, that these angles are 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.

Proof

Two-Column Proof
Let's also show this as a two-column proof.

Statement
Reason
1.
JK ∥ ML, MJ ∥ KL
1.
Given
2.
MK ≅ MK
2.
Reflexive Property of Congruence
3.
∠ JMK ≅ ∠ LKM, ∠ JKM ≅ ∠ LMK
3.
Alternate Interior Angles Theorem
4.
△ MJK ≅ △ KLM
4.
ASA Congruence Theorem