Question

In △LMN and △QRS, m∠L and m∠Q are 55°, and sides
¯¯¯¯¯¯¯
L
M
and
¯¯¯¯¯¯
Q
R
measure 3 inches. Which additional congruence statement proves the triangles are congruent, and with which theorem?

A.
¯¯¯¯¯¯
L
N
≅
¯¯¯¯¯¯
Q
S
, side-side-side

B.
∠N ≅ ∠R, angle-side-angle

C.
∠M ≅ ∠R, angle-side-angle

D.
¯¯¯¯¯¯¯¯
M
N
≅
¯¯¯¯¯
R
S
, side-angle-side

Answer 1

C. With L↔Q and M↔R, if ∠M ≅ ∠R then you have ∠L, side LM, ∠M corresponding to ∠Q, side QR, ∠R, so the triangles are congruent by ASA.