Angles in a Semi-Circle Theorem Study Guide

Definition

When a triangle is inscribed in a semi-circle, the angle subtended by the diameter is a right angle.

Theorem Statement

For a triangle inscribed in a semi-circle, the angle formed by the triangle at the diameter of the semi-circle is a right angle.

Proof

To prove this theorem, we can use the fact that the angle subtended by a diameter of a circle at any point on the circle is a right angle. We can also use the properties of angles in a triangle to show that the angle formed by the triangle at the diameter is a right angle.

Example

Let's consider a semi-circle with a diameter of 10 cm. If a triangle is inscribed in the semi-circle such that one of its vertices is at the endpoint of the diameter and the other two vertices are on the semi-circle, then the angle formed by the triangle at the diameter will be a right angle.

Study Tips

• Understand the properties of angles in a triangle.
• Practice drawing and identifying angles in semi-circles.
• Use the theorem to solve problems involving semi-circles and triangles.