Geometry — Pythagoras' Theorem and Its Converse

About this lesson

This unit focuses on Pythagoras' Theorem and its converse. It begins with a real-world problem about a ladder leaning against a wall, then introduces the theorem, which states that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Students learn to find missing side lengths in right-angled triangles, including the hypotenuse and legs, and to use the converse to determine if a triangle is right-angled. The unit also covers Pythagoras' inequality to classify triangles as acute, obtuse, or right based on side lengths. Worked examples and exercises involve geometric figures such as rectangles, trapeziums, rhombuses, and composite shapes, as well as practical contexts like designing a garden path, a ladder slipping, and a kite. By the end, students should be able to apply the theorem to find lengths, prove triangles are right-angled, classify triangles by angles, and solve problems involving areas and perimeters.