Congruence Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Triangle ABC has sides 3 cm, 4 cm, 5 cm. Triangle DEF has sides 3 cm, 4 cm, 5 cm. Are they congruent?

Solution

  1. 1
    Step 1: Congruent figures have exactly the same size and shape.
  2. 2
    Step 2: Compare corresponding sides: AB=DE=3, BC=EF=4, AC=DF=5.
  3. 3
    Step 3: All three pairs of sides are equal, so by SSS (Side-Side-Side) congruence, the triangles are congruent.
  4. 4
    Step 4: Write the congruence statement: △ABC≅△DEF\triangle ABC \cong \triangle DEF.

Answer

Yes, △ABC≅△DEF\triangle ABC \cong \triangle DEF by SSS.
SSS congruence states that if all three sides of one triangle equal all three sides of another, the triangles must be identical in shape and size. The angles are automatically determined by the side lengths.

About Congruence

Two geometric figures are congruent if they have exactly the same size and shape, so one can be placed on the other perfectly.

Learn more about Congruence →

More Congruence Examples

Example 2 medium

Two rectangles: Rectangle 1 has dimensions 4 cm × 6 cm. Rectangle 2 has dimensions 6 cm × 4 cm. Are

Example 3 easy

Are a square with side 5 cm and a rhombus with side 5 cm necessarily congruent? Explain why or why n

Example 4 hard

Triangle PQR: [formula], [formula], PQ = 8 cm. Triangle XYZ: [formula], [formula], XY = 8 cm. Are th

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