Assignment 7

Problem 7.1

Given a triangle ABC as shown, with points B' on ray AB and C' on ray AC. Suppose that AB' = h AB and AC' = k AC. Then if the area of triangle ABC = T, tell what is the area of triangle AB'C' and prove it. Hint. As an intermediate step, find the area of AB'C in terms of T first and then from there find the final answer. Your answer should agree with what we know about dilation when h = k.

Problem 7.2

Look up the definition of isosceles trapezoid. Suppose that A, B, C, D are points on a circle c and that line AB is parallel to line CD. Prove that ABCD is an isosceles trapezoid.

Problem 7.3

In the figure are two congruent squares. In the first figure is inscribed one circle with a shaded region inside. In the second square are 4 circles, congruent to each other and tangent to the sides and each other as shown. Each of the 4 regions inside the circles is shaded.

In which square is the shaded area larger? Justify your answer..