Episode 7 — Euclidean Geometry

Ratio and Proportion

Learners will be able to:

• Identify the rules and theorems learned in geometry so far that are essential for solving grade 12 Euclidean geometry problems. • Recall and apply the properties of angles around a point, adjacent angles on a straight line, vertically opposite angles, and angles on parallel lines. • Describe the properties of triangles, including the sum of interior angles and exterior angles. • Explain the concept of similarity in triangles and identify corresponding angles and sides. • Apply the ratio theorem to compare quantities with the same units and write ratios in fraction form. • Use proportionality to describe the equality of ratios and solve problems involving similar shapes. • State and apply the proportion theorem, including its converses, to find unknown lengths in similar triangles. • Prove that a line drawn parallel to one side of a triangle divides the other two sides in proportion using the areas of triangles.