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How Can You Use the SSS Theorem to Prove Triangle Congruence?

The SSS (Side-Side-Side) Theorem is a helpful way to show that two triangles are the same size and shape. Here’s how to use it:

  1. Find the Triangles: First, look for the two triangles that you want to compare.

  2. Measure the Sides: Check if all three sides of one triangle are the same as the sides of the other triangle. For example:

    • Triangle A: AB=5AB = 5, AC=7AC = 7, BC=10BC = 10
    • Triangle B: XY=5XY = 5, XZ=7XZ = 7, YZ=10YZ = 10
  3. Decide if They’re Congruent: If AB=XYAB = XY, AC=XZAC = XZ, and BC=YZBC = YZ, then by the SSS Theorem, Triangle A is congruent to Triangle B, which we write as AB\triangle A \cong \triangle B.

This theorem is great because all you need to do is look at the lengths of the sides!

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How Can You Use the SSS Theorem to Prove Triangle Congruence?

The SSS (Side-Side-Side) Theorem is a helpful way to show that two triangles are the same size and shape. Here’s how to use it:

  1. Find the Triangles: First, look for the two triangles that you want to compare.

  2. Measure the Sides: Check if all three sides of one triangle are the same as the sides of the other triangle. For example:

    • Triangle A: AB=5AB = 5, AC=7AC = 7, BC=10BC = 10
    • Triangle B: XY=5XY = 5, XZ=7XZ = 7, YZ=10YZ = 10
  3. Decide if They’re Congruent: If AB=XYAB = XY, AC=XZAC = XZ, and BC=YZBC = YZ, then by the SSS Theorem, Triangle A is congruent to Triangle B, which we write as AB\triangle A \cong \triangle B.

This theorem is great because all you need to do is look at the lengths of the sides!

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