Triangle Congruence help?

Question

1.Triangle M N O and triangle L P O touch only at point O. Angle M O N and L O P are vertical angles. Sides M N L and P are marked parallel. Determine whether the triangles can be proven congruent.

A)Triangle MNO is congruent to triangle PLO by AAS.
B)Triangle MNO is congruent to triangle OLP by SSS.
C)Triangle MNO is congruent to triangle LOP by AAA.
D)Cannot be proven.

2.Triangles L S H and T S H share sides with S H. Side L S and side T S are marked congruent. Side L H and side T H are also marked congruent. Determine whether the triangles can be proven congruent.

A)Triangle HLS is congruent to triangle STH by SSS.
B)Triangle HLS is congruent to triangle THS by SAS.
C)Triangle HLS is congruent to triangle HTS by SSS.
D)Cannot be proven.

Answer 1

1. You can show that the angles are all congruent through vertical angles and parallel lines (opposite interior angles are congruent), but that's the extent of it. This shows you similar triangles (AAA), but not congruence, so the answer is D.

2. All sides are congruent - two are given, and SH is congruent to itself. So you can use SSS for this one - answer is A.