Triangle Congruence Postulates: SAS, ASA & SSS

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  • 0:05 Stacking Triangles
  • 0:45 SSS Postulate
  • 2:13 SAS Postulate
  • 3:27 ASA Postulate
  • 5:13 Lesson Summary
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Lesson Transcript
Instructor: Jeff Calareso

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

When we have two triangles, how can we tell if they're congruent? They may look the same, but you can be certain by using one of several triangle congruence postulates, such as SSS, SAS or ASA.

Stacking Triangles

This is Tricago.

Tricago city line

Times are good in Tricago. Lots of new towers are being built. And each level in each tower is shaped like a triangle. That means that these triangles must by congruent. Congruent Triangles are triangles with three congruent sides and three congruent angles. If two of our triangle levels are congruent, we can always make them stack perfectly and neatly on top of each other.

But how do we know if they're congruent? Let's look at three statements that will tell us, based on what we know about the triangles' sides and angles.

SSS Postulate

First, there's the side-side-side postulate, or SSS. This states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. Should we see this in action? Okay, let's start with an equilateral triangle.

An equilateral triangle has equal sides and equal angles
Equilateral triangle ABC

But what if we add a line from A to the midpoint of BC? Let's call this AD. We now have two smaller triangles: ABD and ACD.

Eqilateral triangle ABC with bisector D

Can we be sure? Well, since ABC is an equilateral triangle, we know angles B and C are each 60 degrees. And angles ADB and ADC are each 90 degrees. Then we split A into BAD and CAD, both of which are 30 degrees. So all three sides and all three angles match. So they are congruent!

So if we're trying to make sure the levels of our building will match, we can measure the three sides. Without even looking at the angles, if the sides all match, the SSS postulate tells us they must be congruent.

SAS Postulate

The SSS postulate is great, but measuring all three sides involves a lot of walking around big triangles. What if you're tired? Is there a shorter way? Yes! There's the Side-Angle -Side postulate, or SAS. This states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Here are two triangles.

Two triangles, ABC and DEF

That's two sides and the included angle. Using the SAS postulate, we know they're congruent. Note that the postulate stipulates the included angle. That means the angle formed by the two sides. If we only knew that angles A and D were equal, that wouldn't be enough. Fortunately, we stopped to measure angles B and E while we were walking around, so we're good.

ASA Postulate

Wait, Tricago is a city of threes, and that's only two postulates. Can we get a third one? It just wouldn't be Tricago if they didn't come in threes.

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