Understanding Worksheet Triangle Sum And Exterior Angle Theorem

What is Triangle Sum And Exterior Angle Theorem?

Triangle Sum And Exterior Angle Theorem is a mathematical theorem that states that the sum of the three angles of a triangle is equal to two right angles, or 180°. It is also known as the Triangle Exterior Angle Theorem or the Triangle Angle-Sum Theorem. This theorem is one of the most important theorems in elementary geometry.

What is the Proof of Triangle Sum And Exterior Angle Theorem?

The proof of the Triangle Sum And Exterior Angle Theorem is as follows: Draw one of the angles of the triangle and draw two straight lines from its vertex to the other two vertices of the triangle. This forms two triangles, each with its own interior angle. Sum the interior angles of both triangles and the exterior angle of the original triangle. The sum of all the angles is equal to two right angles, or 180°.

What Are the Uses of Triangle Sum And Exterior Angle Theorem?

The Triangle Sum And Exterior Angle Theorem can be used to calculate the measure of an angle of a triangle when the other two angles are known. This can be done by subtracting the measure of the two known angles from 180°. It can also be used to prove the existence of a triangle when three angles are given.

Examples of Worksheet Triangle Sum And Exterior Angle Theorem

Consider a triangle ABC with angles A, B and C. If the measure of angle A is 30° and the measure of angle B is 60°, then the measure of angle C can be calculated using the Triangle Sum And Exterior Angle Theorem. The measure of angle C is 90°, since 30° + 60° + 90° = 180°.

Conclusion

The Triangle Sum And Exterior Angle Theorem is an important theorem in elementary geometry. It states that the sum of the angles of a triangle is equal to two right angles, or 180°. This theorem can be used to calculate the measure of an angle of a triangle when the other two angles are known, and to prove the existence of a triangle when three angles are given.