Congruence Math Example 2

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

Example 2

medium
Two rectangles: Rectangle 1 has dimensions 4 cm × 6 cm. Rectangle 2 has dimensions 6 cm × 4 cm. Are they congruent? Explain.

Solution

  1. 1
    Step 1: Congruent figures are the same size and shape, possibly in different orientations.
  2. 2
    Step 2: Rectangle 1: length 6, width 4. Rectangle 2: length 4, width 6.
  3. 3
    Step 3: One is just a 90° rotation of the other. All four sides match if we pair them correctly: 6=66=6 and 4=44=4.
  4. 4
    Step 4: Since all corresponding sides (after rotating) are equal, the rectangles are congruent.

Answer

Yes, the rectangles are congruent — one is a rotation of the other.
Congruence allows rotation, reflection, and translation. Orientation does not affect congruence. Two shapes are congruent as long as all corresponding side lengths and angles match after some rigid transformation.

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 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

← All Congruence Examples Congruence Concept