In this assignment we will discover what type of triangle do we get if we inscribe a triangle in a semicircle. We will use the notion of an isosceles triangle to help us figure this out. An isosceles triangle is one in which two of the sides of the triangle have the same length.
Problem 1. Explain why, the angles a and b in the picture below are equal, and why the angles c and d are equal. Do this by folding the triangle across the height drawn as a dotted line.
Problem 2. Draw a semicircle, and mark the center of the circle. Inscribe a triangle inside it, as in the picture at the top of the page. Show that the triangle is a right triangle by showing that the angle at the top is 90 degrees. To help you do this, draw a radius that ends at this angle; this radius will split the triangle into two smaller triangles. Show that each of the two triangles are isosceles triangles. Use the result of the previous problem to explain why the angle at the top is indeed 90 degrees.