AI generatedGeometry and measuresKS3 / GCSE

Using RHS congruence

Using RHS congruence.

  • Match corresponding vertices and state the equal sides or angles.
  • Use SSS, SAS, ASA or RHS. In SAS the angle must be between the two sides.
  • AAA proves similarity, not congruence. SSA alone is not a congruence test.

Example 1

Prove that triangles ABC and PQR are congruent using the marked information. Lengths are in cm.

Triangle ABCABCDiagram not to scaleTriangle PQRPQRDiagram not to scale
ABC ≅ PQR by RHS.

Both triangles are right-angled, with an equal hypotenuse and one other corresponding side. Match A to P, B to Q and C to R. Orientation does not change congruence.

Example 2

Prove that triangles ABC and PQR are congruent using the marked information. Lengths are in cm.

Triangle ABCABCDiagram not to scaleTriangle PQRPQRDiagram not to scale
ABC ≅ PQR by RHS.

Both triangles are right-angled, with an equal hypotenuse and one other corresponding side. Match A to P, B to Q and C to R. Orientation does not change congruence.

Your turn

Question 1

Prove that triangles ABC and PQR are congruent using the marked information. Lengths are in cm.

Triangle ABCABCDiagram not to scaleTriangle PQRPQRDiagram not to scale
Check answer
ABC ≅ PQR by RHS.

Both triangles are right-angled, with an equal hypotenuse and one other corresponding side. Match A to P, B to Q and C to R. Orientation does not change congruence.

Question 2

Prove that triangles ABC and PQR are congruent using the marked information. Lengths are in cm.

Triangle ABCABCDiagram not to scaleTriangle PQRPQRDiagram not to scale
Check answer
ABC ≅ PQR by RHS.

Both triangles are right-angled, with an equal hypotenuse and one other corresponding side. Match A to P, B to Q and C to R. Orientation does not change congruence.

Question 3

Prove that triangles ABC and PQR are congruent using the marked information. Lengths are in cm.

Triangle ABCABCDiagram not to scaleTriangle PQRPQRDiagram not to scale
Check answer
ABC ≅ PQR by RHS.

Both triangles are right-angled, with an equal hypotenuse and one other corresponding side. Match A to P, B to Q and C to R. Orientation does not change congruence.

Question 4

Prove that triangles ABC and PQR are congruent using the marked information. Lengths are in cm.

Triangle ABCABCDiagram not to scaleTriangle PQRPQRDiagram not to scale
Check answer
ABC ≅ PQR by RHS.

Both triangles are right-angled, with an equal hypotenuse and one other corresponding side. Match A to P, B to Q and C to R. Orientation does not change congruence.

Question 5

Prove that triangles ABC and PQR are congruent using the marked information. Lengths are in cm.

Triangle ABCABCDiagram not to scaleTriangle PQRPQRDiagram not to scale
Check answer
ABC ≅ PQR by RHS.

Both triangles are right-angled, with an equal hypotenuse and one other corresponding side. Match A to P, B to Q and C to R. Orientation does not change congruence.

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