Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
1-4. Quiz
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Exercise 8 Page 616

SAS Congruence Theorem means that two sides and the included angle of two triangles are congruent.

There is enough information.
Proof: See solution.

Practice makes perfect

According to the SAS Congruence Theorem, if two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

What do we know about our triangles?

Examining the diagram, we see that our triangles share MP as a side. Therefore, by the Reflexive Property of Congruence, these sides are congruent. Let's add this information to the diagram.

Can we use SAS?

Since two sides and the included angle of △ LMP are congruent with two sides and the included angle of △ NMP, we can prove congruence by the SAS Congruence Theorem.

Two-column proof

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

Statement
Reason
1.
LM ≅ NM, ∠ LMP ≅ ∠ NMP
1.
Given
2.
MP≅ MP
2.
Reflexive Property of Congruence
3.
△ LMP ≅ △ NMP
3.
SAS Congruence Theorem