How to prove triangles are congruent SAS and HL

Get the most by viewing this topic in your current grade. Pick your course now.

Write a two-column proof.
1. Given: R is the midpoint of $\overline {MP}$ .
  R is the midpoint of $\overline {NQ}$ .
  Prove: $\triangle MRN$ $\cong$ $\triangle PRQ$
2. Special case for right triangle:
  Given: $\triangle ABC$ is an isosceles triangle.
  D is the midpoint of $\overline {AC}$ .
  Prove: $\triangle ABD$ $\cong$ $\triangle CBD$ .
Write a flow proof
1. Given: R is the midpoint of $\overline {MP}$ .
  R is the midpoint of $\overline {NQ}$ .
  Prove: $\triangle MRN$ $\cong$ $\triangle PRQ$
2. Special case for right triangle:
  Given: $\triangle ABC$ is an isosceles triangle.
  D is the midpoint of $\overline {AC}$ .
  Prove: $\triangle ABD$ $\cong$ $\triangle CBD$ .
Is there enough information given to prove the following triangles are congruent? If so, explain your reasoning and point out the theorem or postulate you use.