SAS Congruence Exploration
Table of Contents
- Exploration
- SAS Congruence Exploration
- Theorem and Proofs
- Theorem and Proof
SAS Congruence Exploration
Play around with the triangles and figure out which each slider does. Also be sure to move the vertices of the triangles and take note of what happens :)
What do you notice about the two triangles? Are there any similarities or differences?
Side AB is congruent to side A'B' and side BC is congruent to side B'C'. Angles ABC and A'B'C' are also congruent. Play around with the points for a few minutes before answering the question below.
Is it possible to make a second triangle that is different from the first?
If there are two triangles that have two congruent sides with a congruent angle in the middle of the two sides, will the third sides be sometimes, never, or always congruent?
Justify your response above.
Theorem and Proof
[b][u]Theorem 4-3: Side-Angle-Side (SAS) Congruence Criterion[br][br][/u][/b]If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
We are only exploring Side-Angle-Side (SAS) today but there will be many different congruence laws that we will be exploring this week. In all of the laws the S will stand for side and the A will stand for angle. Other laws for later are SSS, ASA, and AAS. All of these laws can be used to show two triangles are congruent.
Recognizing SAS Congruence
Working left to right, determine if the triangle pairs are congruent using SAS
Proof?? What is that??
We want to prove that triangle BCA is Congruent to triangle ECD. Using the given informtion, ideas explored in class today, as well as your previous knowledge, write a couple sentences explaining whether or not the triangles are congruent.
Mathematicians like to keep these short so another way to demonstrate a proof is using a two-column proof. Together we will go through the example on your notes and then you will complete the exit ticket!