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Big Ideas Math Integrated I, 2016 View details

6. Proving Triangle Congruence by ASA and AAS

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Exercise 20 Page 631

Notice that the two triangles share a side, KM.

See solution.

Practice makes perfect

Examining the diagram, we see that the two triangles share a side, KM. By the Reflexive Property of Congruence, we know this side is congruent in our triangles. Let's separate the triangles and add this information to the diagram.

Now we have enough information to claim congruence by the AAS Congruence Theorem.

Alternative Solution

Two-Column Proof

Let's show this as a two-column proof.

Statement	Reason
1. ∠ NKM ≅ ∠ LMK, ∠ L ≅ ∠ N	1. Given
2. KM≅ KM	2. Reflexive Property of Congruence
3. △ NMK ≅ △ LKM	3. AAS Congruence Theorem