Geometry Questions with Solutions

Geometry in entrance exams covers lines and angles, triangles, quadrilaterals, polygons and circles. Questions test properties of angles formed by parallel lines, congruence and similarity of triangles, the Pythagorean theorem, properties of special quadrilaterals, interior and exterior angles of polygons, and circle theorems such as angles in the same segment and tangent properties. Most geometry questions are solved by recognising the right property, not by long calculation. A neat rough diagram, labelled with the given information, often reveals the answer. Pythagorean triplets (3-4-5, 5-12-13, 8-15-17) and the 30-60-90 and 45-45-90 triangle ratios are worth memorising because they appear repeatedly. Practise the geometry questions below. Each comes with a step-by-step solution that names the property used.