SAS (Side-Angle-Side) Congruence

Suppose we have to prove that two triangles are congruent.

And the given was that angle A is congruent to angle D, and angle B is congruent to angle E. So the ASA theorem states that if two triangles have a congruent angle, then a congruent side, then finally another different congruent angle, then they are congruent.

It's not exactly easy to use this theorem. Sometimes you have to prove to congruent triangles who share a side, so you kind of have to dumbly state using the reflexive property that some line/segment is congruent to itself.

Now we are dealing with SAS. To prove these triangles congruent, we have to...

...know that a side, an angle, and a side on two different triangles are congruent. Yes, if you're wondering, the order of the sides and angle have to be in exactly that order otherwise it'll be called something else like $SSA$.

So anyway, just as a side note, congruence theorems like ASA, SSS, SAS, and SSA only work on triangles.

Please do problems 1, 5, 7, 9, 12, 13, 15, and 18 on this worksheet as practice for SAS congruence. GLHF!

For extra practice, please do problems 1, 2, 3, 4, 8, 9, 10, 11, 12, 15, 17, and 18 on this worksheet. Have fun!

Here is a great triangle drawing tool that can help you out in this topic.