Which shows two triangles that are congruent by the sss congruence theorem?

General
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which shows two triangles that are congruent by the sss congruence theorem?

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Which shows two triangles that are congruent by the SSS congruence theorem?

Answer: To determine which triangles are congruent by the SSS (Side-Side-Side) congruence theorem, you need to verify that all three corresponding sides of one triangle are equal in length to all three corresponding sides of another triangle. This theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Here’s how you can identify such triangles:

  1. Identify the Corresponding Sides: Look at the two triangles and identify the three sides of each triangle. Label these sides for clarity, such as (a, b, c) for the first triangle and (d, e, f) for the second triangle.

  2. Compare the Lengths of the Corresponding Sides: Measure or note the lengths of the sides. Ensure that:

    • Side (a) of the first triangle is equal to side (d) of the second triangle.
    • Side (b) of the first triangle is equal to side (e) of the second triangle.
    • Side (c) of the first triangle is equal to side (f) of the second triangle.

  3. Confirm Congruence: If all three pairs of corresponding sides are equal in length, then the two triangles are congruent by the SSS theorem.

Example:

Consider the following two triangles:

  • Triangle 1 has sides of lengths 5 cm, 7 cm, and 10 cm.
  • Triangle 2 has sides of lengths 5 cm, 7 cm, and 10 cm.

Since all three sides of Triangle 1 are equal in length to the corresponding sides of Triangle 2, the triangles are congruent by the SSS congruence theorem.

Visual Representation:

If you have a diagram, it would look something like this:

Triangle 1:

  • Side (AB = 5) cm
  • Side (BC = 7) cm
  • Side (CA = 10) cm

Triangle 2:

  • Side (DE = 5) cm
  • Side (EF = 7) cm
  • Side (FD = 10) cm

Since (AB = DE), (BC = EF), and (CA = FD), the triangles are congruent by the SSS theorem.

In summary, to show that two triangles are congruent by the SSS theorem, you need to ensure that all three sides of one triangle are equal in length to the corresponding sides of another triangle.