Side-Side-Side (SSS) Triangle: Formula & Theorem

Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Side-side-side triangles are often found in geometric proofs. In this lesson, learn about the side-side-side postulate, and review what you've learned with a quiz.

What is Congruent?

Often in mathematics - specifically in geometry - you will be asked to determine if certain shapes, angles, and/or sides are congruent. Congruent means that two or more things are the same measurement. In geometry, proving that shapes, angles, and/or sides are congruent can help you find the measurements of other shapes, angles, or sides.

What are SSS Triangles?

Side-side-side triangles, or SSS triangles, are two triangles that have corresponding sides of the same size (the corresponding sides are congruent). Once you find that two triangles are SSS triangles, then you can find out a lot more information about those triangles, like the measurements of the angles.

Congruent Sides and Angles

SSS Triangles with Tick Marks
SSS Triangles with Tick Marks

In the above image, you might have noticed that each triangle has one, two, or three lines going through each of its sides. These little lines are called tick marks. In geometry, tick marks indicate congruent measurements.

For example, we can tell that line AC and line XY are congruent because they both have one tick mark. Angle ACB and angle YXZ are also congruent because they each have two tick marks. So, looking at the above image, which sides and which angles are congruent based on the number of tick marks? Here are the answers:

  • Sides: AC & XY, AB & YZ, BC & XZ
  • Angles: XYZ & CAB, ACB & YXZ, ABC & YZX

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