Triangle Congruence Postulates - SSS & SAS Explained (2019)

Did you know that there are five ways you can prove triangle congruency?

Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)

It’s true!

In today’s geometry lesson, we’re going to tackle two of them, the Side-Side-Side and Side-Angle-Side postulates.

You’ll quickly learn how to prove triangles are congruent using these methods.

In addition, you’ll see how to write the associated two column proof.

Let’s jump in!

So we already know, two triangles are congruent if they have the same size and shape. This means that the pair of triangles have the same three sides and the same three angles (i.e., a total of six corresponding congruent parts).

Thankfully we don’t need to prove all six corresponding parts are congruent… we just need three!

Why?

Because if we can show specific sides and/or angles to be congruent between a pair of triangles, then the remaining sides and angles are also equal.

But there is a warning; we must be careful about identifying the accurate side and angle relationships!

As Math is Fun accurately states, there only five different congruence postulates that will work for proving triangles congruent. So we need to learn how to identify congruent corresponding parts correctly and how to use them to prove two triangles congruent.

Triangle Congruence Postulates

The first two postulates, Side-Angle-Side (SAS) and the Side-Side-Side (SSS), focus predominately on the side aspects, whereas the next lesson discusses two additional postulates which focus more on the angles. Those are the Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) postulates.

Side-Angle-Side

If we can show that two sides and the included angle of one triangle are congruent to two sides and the included angle in a second triangle, then the two triangles are congruent.

This is called the Side Angle Side Postulate or SAS. And as seen in the image, we prove triangle ABC is congruent to triangle EDC by the Side-Angle-Side Postulate

SAS Postulate Example

Side-Side-Side

Or, if we can determine that the three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

We refer to this as the Side Side Side Postulate or SSS. And as seen in the image to the right, we show that trianlge ABC is congruent to triangle CDA by the Side-Side-Side Postulate.

SSS Postulate Example

I’m confident that after watching this lesson you will agree with me that proving triangles congruent is fun and straightforward.

Triangle Congruency – Lesson & Examples (Video)

38 min

• Introduction to triangle congruency lesson
• 00:00:13 – What are SAS and SSS Postulates?
• 00:07:20 – Are the triangles congruent by SAS? (Examples #1-3)
• Exclusive Content for Member’s Only

• 00:13:58 – Are the triangles congruent by SSS? (Examples #4-6)
• 00:18:12 – Write SAS, SSS or Not Congruent (Examples #7-12)
• 00:32:20 – Complete the two-column proof (Example #13)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

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