Equiangular Triangles — O/L Mathematics

What must I remember about Equiangular Triangles?

• Equiangular Triangles Definition: Two triangles are equiangular if the three interior angles of one triangle are respectively equal to the three interior angles of the other triangle.
• Similarity Criterion (AAA): If two triangles are equiangular, their corresponding sides are proportional, and the triangles are SIMILAR (ΔABC ~ ΔPQR).
• Ratio of Corresponding Sides: In similar equiangular triangles: AB / PQ = BC / QR = AC / PR = k (constant ratio of similarity).
• Right-Angled Triangle Similarity: The altitude drawn from the right-angled vertex to the hypotenuse divides the triangle into two sub-triangles that are similar to the original triangle and to each other.

Test yourself (1 minute)

1. Correct pairing of corresponding sides

   Corresponding sides are ALWAYS opposite EQUAL ANGLES; write angle equality first before forming side ratios.

2. Two angles equality is sufficient (AA)

   If two angles of one triangle equal two angles of another, the third angles are automatically equal (sum = 180°), proving equiangularity.

3. Cross-multiplication in side ratios

   If AB / PQ = BC / QR, then AB × QR = BC × PQ; standard algebraic method to prove geometric product relations in Paper 2 geometry riders.

Practise Equiangular Triangles questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 11, Unit 14)

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Where does Equiangular Triangles fit in the syllabus?

Grade 11 · Term 2