Assignment 5B (due Monday, 10/25)

These problems are the results of Lab 4.

Problem 5.1: Prove: If AB is a diameter of a circle, and C is a point on the circle distinct from A and B, prove that angle ACB is a right angle.

Problem 5.2: Prove: If ABC is a triangle with angle C a right angle, prove that the point C is on the circle with diameter AB.

Assignment 5C (Due Wednesday 10/27)

Problem 5.3: Given the segment of length 1 and segments of length a and b below:

1. Construct a segment c of length a/b.

2. Construct a segment d of length ab.

Problem 5.4: Given an arbitrary triangle ABC, construct points B' on AB and C' on AC so that B'C' is parallel to BC and also so that triangle AB'C' has area equal one-half of the area of triangle ABC.

· What is the ratio of the perimeter of AB'C' to the perimeter of ABC?

Problem 5.5: Berele-Goldman, Problem 4.9 - Proves that the "scaling" of points on a line is another line.

Problem 5.6: Let ABC be a triangle and let B' be a point on AB and C' a point on AC with |AB'|/|AB| = |AC'|/|AC|.

If M is the midpoint of BC and N is the intersection of line AM with line B'C', prove that N is the midpoint of B'C'.