Equiangular Triangles — O/L Mathematics

How do I practise Equiangular Triangles?

1 question with a worked solution

1. Triangles ABC and PQR are equiangular (similar) with angle A = angle P, angle B = angle Q, and angle C = angle R. If AB = 8 cm, PQ = 12 cm, and BC = 10 cm, find the length of QR.
   1. A) 16 cm
   2. B) 13.5 cm
   3. C) 14 cm
   4. D) 15 cm
   Check my answer

   Correct answer: D) 15 cm

   In equiangular triangles, the ratios of corresponding sides are equal: AB/PQ = BC/QR → 8/12 = 10/QR → 2/3 = 10/QR → QR = (10 × 3)/2 = 15 cm.

   Show worked solution

   Step 1: Set up proportionality ratio: AB / PQ = BC / QR. Step 2: Substitute given lengths: 8 / 12 = 10 / QR. Step 3: Simplify fraction: 2 / 3 = 10 / QR. Step 4: Solve for QR: 2 × QR = 30 → QR = 15 cm. Answer: 15 cm.
   Modelled on: the O/L Mathematics examination pattern

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Where does Equiangular Triangles fit in the syllabus?

Grade 11 · Term 2