<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation

SSS Triangle Congruence

Three sets of equal side lengths determine congruence.

Atoms Practice
Estimated6 minsto complete
%
Progress
Practice SSS Triangle Congruence
 
 
 
MEMORY METER
This indicates how strong in your memory this concept is
Practice
Progress
Estimated6 minsto complete
%
Practice Now
Turn In
My SSS Triangle Congruence

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.

  1. Use SSS
  2. Use SSS

Fill in the blanks in the proofs below.

  1. Given: is the midpoint of Prove:
Statement Reason
1. 1.
2. 2. Definition of a Midpoint
3. 3. Reflexive PoC
4. 4.

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / Notes
Show More

Image Attributions

Explore More

Sign in to explore more, including practice questions and solutions for SSS Triangle Congruence.
Please wait...
Please wait...