Practice Maths

Congruent Figures — Solutions

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  1. Identify congruent figures

    1. Two 6 cm squares:
    2. 4×7 and 7×4 rectangles:
    3. Triangles 3,4,5 and 3,4,6:
    4. Two circles radius 5 cm:
    5. Same angles, different side lengths:
    6. Two equilateral triangles side 9 cm:

  2. Corresponding parts of ▵ABC ≅ ▵PQR

    1. PQ:
    2. QR:
    3. PR:
    4. ∠P:
    5. ∠Q:
    6. ∠R:

  3. Name the congruence test

    1. Sides 5, 8, 10:
    2. Two sides 6, 9 and included angle 48°:
    3. Angles 35° and 75°, side between them 7 cm:
    4. Right angle, hypotenuse 13, leg 5:
    5. Same angles, different sides:
    6. Two equal angles, non-corresponding side:
    7. Right-angled, legs 4 and 3:
    8. Two sides, non-included angle:

  4. Find unknown values using congruence

    1. KL = ST:
    2. ∠D = ∠G:
    3. AC = XZ, AB = XY:
    4. AB = CB:
    5. ∠P = ∠L, ∠Q = ∠M, so ∠R = ∠N:

  5. Congruence proofs

    1. SSS proof:
    2. SAS proof:
    3. AAS proof:
    4. RHS proof:

  6. Problem solving with congruence

    1. Ladder triangles:
    2. Rectangle diagonal:
    3. Garden beds:
    4. Two equal angles:

  7. Algebraic congruence — find unknowns

    1. ▵ABC ≅ ▵PQR:
    2. ▵DEF ≅ ▵GHI:
    3. Isosceles triangle ABM and ACM:
    4. ▵KLM ≅ ▵NOP:

  8. Congruence proof from shape properties

    1. Parallelogram ABCD, diagonal AC:
    2. Right-angled triangles RHS proof:
    3. Kite ABCD, diagonal BD:
    4. Triangles XYZ and MNO:

  9. Real-world congruence

    1. Bridge truss triangles:
    2. Tile cut diagonally:
    3. Same area ≠ congruent:
    4. River width survey:

  10. Extended congruence reasoning

    1. RHS proof:
    2. Square ABCD diagonal AC:
    3. Triangles with same base, apices on parallel line:
    4. Congruent vs similar: