# Triangles congruent by SAS and HL proofs

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##### Intros
###### Lessons
1. Similar tirangles VS. Congruent triangles
2. Ways to prove congruency:
• SSS
• SAS
• ASA
• AAS
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##### Examples
###### Lessons
1. 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$.

2. 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$.

3. 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.