http://www.ck12.org Chapter 4. Triangles and Congruence
- Connect the two endpoints by drawing the third side.
Can you draw another triangle, with these measurements that looks different? The answer is NO.Only one triangle
can be created from any given two lengths and the INCLUDED angle.
Side-Angle-Side (SAS) Triangle Congruence Postulate:If two sides and the included angle in one triangle are
congruent to two sides and the included angle in another triangle, then the two triangles are congruent.
The markings in the picture are enough to say that 4 ABC∼= 4 XY Z.
So, in addition to SSS congruence, we now have SAS. Both of these postulates can be used to say that two triangles
are congruent. When doing proofs, you might be able to use either SSS or SAS to prove that two triangles are
congruent. There is no set way to complete a proof, so when faced with the choice to use SSS or SAS, it does not
matter. Either would be correct.
Example 3:What additional piece of information would you need to prove that these two triangles are congruent
using the SAS Postulate?
a)^6 ABC∼=^6 LKM
b)AB∼=LK
c)BC∼=KM
d)^6 BAC∼=^6 KLM
Solution:For the SAS Postulate, you need two sides and the included angle in both triangles. So, you need the side
on the other side of the angle. In 4 ABC, that isBCand in 4 LKMthat isKM. The correct answer is c.
Example 4:Write a two-column proof to show that the two triangles are congruent.
Given:Cis the midpoint ofAEandDB
Prove: 4 ACB∼= 4 ECD