4.7. SAS Triangle Congruence http://www.ck12.org
Example C
Is the pair of triangles congruent? If so, write the congruence statement and why.
While the triangles have two pairs of sides and one pair of angles that are congruent, the angle is not in the same place
in both triangles. The first triangle fits with SAS, but the second triangle is SSA. There is not enough information
for us to know whether or not these triangles are congruent.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter4SASTriangleCongruenceB
Vocabulary
Two figures arecongruentif they have exactly the same size and shape. By definition, two triangles arecongruent
if the three corresponding angles and sides are congruent. The symbol∼=means congruent. There are shortcuts for
proving that triangles are congruent. TheSAS Triangle Postulatestates that 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.
Guided Practice
- Is the pair of triangles congruent? If so, write the congruence statement and why.
- State the additional piece of information needed to show that each pair of triangles is congruent.
- Fill in the blanks in the proof below.
Given:
AB∼=DC,BE∼=CE
Prove: 4 ABE∼= 4 ACE
TABLE4.8:
Statement Reason
- 2.^6 AEB∼=^6 DEC 2.
- 4 ABE∼= 4 ACE 3.
Answers:
The pair of triangles is congruent by the SAS postulate. 4 CAB∼= 4 QRS.
We know that one pair of sides and one pair of angles are congruent from the diagram. In order to know that the
triangles are congruent by SAS we need to know that the pair of sides on the other side of the angle are congruent.
So, we need to know thatEF∼=BA.