Geometry Problems

Geometry Problems: Types and Techniques

Properties of Lines and Angles

Parallel lines are always the same distance apart and will never touch or intersect.
If two angles in one place are formed by two straight lines intercepted by a thirdthey, they are referred to as vertically opposite angles. These angles are always equal.
Adjacent angles are those angles that share a common arm. The sum of adjacent angles on a straight line equals 180°, often referred to as the linear pair.

Triangle Properties

Triangles have three sides and the sum of their angles always equals 180°.
Isosceles triangles have two sides of the same length and the angles opposite these sides are equal.
Equilateral triangles have all sides and all angles equal, with each angle measuring 60°.
Right-angled triangles have one angle measuring 90°.

Quadrilaterals and their Properties

All quadrilaterals (four-sided shapes) have angles that add up to 360°.
A rectangle has four right angles and opposite sides are equal.
A square is a type of rectangle with all sides equal.
The diagonals of a parallelogram are not of equal length, but they bisect each other at right angles.
The diagonals of a rectangle are equal in length and bisect each other, but they do not form right angles.

Circle Geometry

A line segment drawn from one point on the circle to another is a chord.
Diameter is a chord that passes through the centre of the circle.
A radius is a line segment joining the centre of the circle to any point on the circle.
Tangent is a line touching the circle at exactly one point.
In a circle, the central angle corresponding to a given arc is twice the size of the angle at the circumference.

Solving Geometry Problems

To solve problems in geometry, draw diagrams wherever necessary to understand the problem better.
Use geometric rules and properties to help find missing angles or sides.
Always check your solutions to ensure they make sense in context of the problem.