Equiangular Triangles

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Grade 11 · Term 2

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About O/L Mathematics: O/L Mathematics covers number systems, algebra, geometry, trigonometry, and statistics across Grade 10 and 11.

• Angle Sum of a Triangle: The sum of the interior angles of any triangle is 180 degrees
• If a triangle is equiangular, each angle = 180/3 = 60 degrees
• AA Similarity Criterion: If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar (equiangular)
• This is sufficient because the third angles will automatically be equal
• Proportionality of Sides in Similar Triangles: If triangle ABC is similar to triangle PQR (equiangular), then:

Must know

• Always state the similarity criterion: When proving two triangles are equiangular, explicitly mention which angles are equal and why (e.g., common angle, corresponding angles from parallel lines, vertically opposite angles, right angles). Use the AA criterion
• Write proportions clearly: After establishing similarity, write the proportion of corresponding sides in a clear, ordered manner. For example, if triangle ABC is similar to triangle DEF, write AB/DE = BC/EF = CA/FD
• Use the Basic Proportionality Theorem efficiently: If a line is parallel to a side, you can directly use the ratios without proving similarity each time. But be sure to state the theorem
• Check for right angles: In many problems, right angles are given or implied (e.g., vertical objects, perpendicular lines). Use them to establish equiangularity

Source: Idasara knowledge pack — english/OL_11/mathematics v16, short_notes: Lesson 14 - Equiangular Triangles

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