Congruence Math Example 3

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

Example 3

easy
Are a square with side 5 cm and a rhombus with side 5 cm necessarily congruent? Explain why or why not.

Solution

  1. 1
    Step 1: Check both size and shape. Both have 4 sides each of length 5 cm.
  2. 2
    Step 2: A square has all right angles (90°). A rhombus can have angles other than 90°.
  3. 3
    Step 3: If the angles differ, the shapes are different, so they are NOT necessarily congruent.

Answer

Not necessarily congruent — they could have different angles.
Congruence requires both the same size AND the same shape. Equal side lengths alone are not enough for quadrilaterals; the angles must also match. SSS congruence guarantees angle matching for triangles but not for polygons with more sides.

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 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

Example 2 medium

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

Example 4 hard

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

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