G.2.6.2 Proving the Side-Angle-Side Triangle Congruence Theorem

Two triangles have 2 pairs of corresponding sides congruent, and the corresponding angles between those sides are congruent. The two 2 triangles are LMN and PQR, so that:

  • Segment LM is congruent to segment PQ
  • Segment LN is congruent to segment PR
  • Angle L is congruent to angle P
LN and PR are congruent so there is a sequence of rigid motion that takes LN onto PR. Perform and precisely describe that sequence of rigid motions.

Now two of the corresponding points coincide because of the rigid transformation we already performed. What about the third pair of corresponding points? Why do they not coincide? Explain how you know.

Why will a reflection get the third pair of corresponding points to coincide?

Now that all three corresponding vertices coincide what do we know about the triangles?