What if you were given two triangles and provided with information only about their side lengths? How could you determine if the two triangles were congruent? After completing this concept, you'll be able to use the Side-Side-Side (SSS) shortcut to prove triangle congruency.
Guidance
If 3 sides in one triangle are congruent to 3 sides in another triangle, then the triangles are congruent.
, and then .
This is called the Side-Side-Side (SSS) Postulate and it is a shortcut for proving that two triangles are congruent. Before, you had to show 3 sides and 3 angles in one triangle were congruent to 3 sides and 3 angles in another triangle. Now you only have to show 3 sides in one triangle are congruent to 3 sides in another.
Example A
Write a triangle congruence statement based on the picture below:
From the tic marks, we know . From the SSS Postulate, the triangles are congruent. Lining up the corresponding sides, we have .
Don’t forget ORDER MATTERS when writing congruence statements. Line up the sides with the same number of tic marks.
Try the following example:
Problem 1:
Is the pair of triangles congruent? If so, write the congruence statement and why.
Answers on bottom of page!
Example B
Write a two-column proof to show that the two triangles are congruent.
Given :
is the midpoint of and .
Prove :
Statement | Reason |
---|---|
1. is the midpoint of and |
1.Given |
2. | 2.Definition of a midpoint |
3. | 3.SSS Postulate |
Note that you must clearly state the three sets of sides are congruent BEFORE stating the triangles are congruent.
Here is a video explanation of this problem:
Try the following example:
2. Fill in the blanks in the proof below.
Given :
Prove :
Statement | Reason |
---|---|
1. | 1. |
2. | 2. Reflexive PoC |
3. | 3. |
Answers on bottom of page!
Answers:
1. The triangles are congruent because they have three pairs of sides congruent. .
2.
Statement | Reason |
---|---|
1. | 1. Given |
2. | 2. Reflexive PoC |
3. | 3. SSS Postulate |
HOMEWORK:
Are the pairs 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.
- Use SSS
- Use SSS
Fill in the blanks in the proofs below.
- Given : is the midpoint of Prove :
Statement | Reason |
---|---|
1. | 1. |
2. | 2. Definition of a Midpoint |
3. | 3. Reflexive PoC |
4. | 4. |