Geometry and Trigonometry 1

Section 1Angle basics

Angles on a straight line add to 180 degrees, and angles around a point add to 360 degrees. Vertically opposite angles are equal. These facts are quick marks when a diagram gives only one or two angle values.

Section 2Parallel-line angles

When a transversal crosses parallel lines, corresponding angles are equal, alternate angles are equal, and co-interior angles add to 180 degrees. Watch out: the parallel lines must actually be marked or stated. Do not assume lines are parallel just because they look that way.

Section 3Polygons

A polygon is a closed shape made from straight sides. The sum of interior angles in an n-sided polygon is (n - 2) x 180 degrees. For a regular polygon, all sides and all interior angles are equal.

Section 4Congruency

Congruent shapes are identical in shape and size. They may be turned, flipped, or moved, but matching sides and angles are equal. Common triangle congruency tests include SSS, SAS, ASA, and RHS for right-angled triangles.

Section 5Similarity

Similar shapes have the same shape but not necessarily the same size. Their matching angles are equal, and corresponding sides are in the same ratio. Here's the trick: similar shapes use a scale factor, so lengths scale directly but areas scale by the square of the scale factor.

Section 6Circle parts

A radius goes from the centre to the circumference, while a diameter goes across the circle through the centre. A chord joins two points on the circumference. A tangent touches the circle at exactly one point.

Section 7Circle angle facts

An angle at the centre is twice the angle at the circumference standing on the same arc. An angle in a semicircle is 90 degrees. The angle between a tangent and a radius at the point of contact is 90 degrees.