# An Angle Bisector in a Right Triangle

Given a right triangle ABC (∠B = 90o ) with ∠A = 60o . Point M lies on BC so that BM = 0.5 MC (Figure 1). Prove that AM is an angle bisector in triangle ABC

.Answer the following questions to reason why AM bisects angle A. What kind of triangle is ACA'?

• How is the line CB related to the line AA'?

• What is the point M called in relation to the triangle ACA'?

• How is M related to the vertices of the triangle ACA'?

• How is M related to the angles of the triangle ACA'?

• Would this hold if angle A was not equal to 60 degrees?

**Victor Oxman,** Western Galilee College, Israel

**Moshe Stupel**, Gordon Education College and Shaanan – The Religious Education College, Haifa, Israel.