AI generatedGeometry and measuresKey Stage 3

Proving triangles similar

Proving triangles similar.

  • Give a mathematical reason for each step.
  • Use matching angles and corresponding sides, not the appearance of a diagram.
  • State the result you have proved at the end.

Example 1

Prove that ABC and PQR are similar.

Geometry diagramABCDiagram not to scaleGeometry diagramPQRDiagram not to scale
ABC ∼ PQR by AA.

Angles A and P are equal; angles B and Q are equal. Two matching angles establish similarity. Corresponding sides are proportional, rather than necessarily equal.

Example 2

Prove that ABC and PQR are similar.

Geometry diagramABCDiagram not to scaleGeometry diagramPQRDiagram not to scale
ABC ∼ PQR by AA.

Angles A and P are equal; angles B and Q are equal. Two matching angles establish similarity. Corresponding sides are proportional, rather than necessarily equal.

Your turn

Question 1

Prove that ABC and PQR are similar.

Geometry diagramABCDiagram not to scaleGeometry diagramPQRDiagram not to scale
Check answer
ABC ∼ PQR by AA.

Angles A and P are equal; angles B and Q are equal. Two matching angles establish similarity. Corresponding sides are proportional, rather than necessarily equal.

Question 2

Prove that ABC and PQR are similar.

Geometry diagramABCDiagram not to scaleGeometry diagramPQRDiagram not to scale
Check answer
ABC ∼ PQR by AA.

Angles A and P are equal; angles B and Q are equal. Two matching angles establish similarity. Corresponding sides are proportional, rather than necessarily equal.

Question 3

Prove that ABC and PQR are similar.

Geometry diagramABCDiagram not to scaleGeometry diagramPQRDiagram not to scale
Check answer
ABC ∼ PQR by AA.

Angles A and P are equal; angles B and Q are equal. Two matching angles establish similarity. Corresponding sides are proportional, rather than necessarily equal.

Question 4

Prove that ABC and PQR are similar.

Geometry diagramABCDiagram not to scaleGeometry diagramPQRDiagram not to scale
Check answer
ABC ∼ PQR by AA.

Angles A and P are equal; angles B and Q are equal. Two matching angles establish similarity. Corresponding sides are proportional, rather than necessarily equal.

Question 5

Prove that ABC and PQR are similar.

Geometry diagramABCDiagram not to scaleGeometry diagramPQRDiagram not to scale
Check answer
ABC ∼ PQR by AA.

Angles A and P are equal; angles B and Q are equal. Two matching angles establish similarity. Corresponding sides are proportional, rather than necessarily equal.

← All Geometry and measures cardsReport a mistake