Assignments for Week 2

Reading for Week 2

B&B, Chapter 2.

This chapter starts with the basic Ruler and Protractor Axioms that give the assumed properties of lines and angles. It also states SAS axiom for similar triangles. This completes the set of plane geometry axioms for B&B.

B&B, Chapter 3.

This chapter is full of basic facts and tools, centered around Principles 6-12. Two of these principles are ASA and SSS for similar triangles, which we will assume without going through the proof. Some of this chapter we discussed in Week 1. The locus theorem for perpendicular bisectors is here as well as the Pons Asionorum about isosceles triangles. New theorems include the basic angle sum for triangles and the Pythagorean Theorem.

Heilbron, pp 61-63 and parts of GTC lab book, Chaps 2 and 3

Read about loci.

Exercises 3 (Due Wed 10/6)

E3.1. Constructing Ratios

Draw a random segment AB on a sheet of paper and use a straightedge and compass to construct a point C on AB so that AC/AB = 3/5.

E3.2. Subtriangles of a right triangle.

Let triangle ABC be a triangle, with angle C being a right angle. Let D be the foot of the altitude through C (i.e., D is the point on AB for which line CD is perpendicular to line AB). If the lengths of the sides of triangle ABC are |AB| = c. |BC| = a, |CA| = b, find the lengths of segments CD, AD, and BD (in terms of a, b, c. Give reasons.

E3.3. SSA or ASS?

Construct two non-congruent triangles which satisify the SSA criterion. Hint: Read Heilbron, p. 55 and look at a figure at the bottom of the page.

Exercises 4 (Due Fri 10/8)

E4.1. Constructing Ratios

Draw a random segment AB on a sheet of paper and use a straightedge and compass to construct a point C on AB so that AC/AB = square root of 3/5.

E4.2 Exterior angles of a triangle..

Prove B&B page 84 #2. Then figure out the angle sum of the exterior angles of a triangle.

E4.3. Hypotenuse-Leg

B&B page 85, #12 and #13

Assignment 2 (70 points, Due Mon 10/11)

In these proofs you can use the triangle similarity criteria and the other theorems (Principles 1-12) in Chapters 2-3 of B&B.

2.1 Altitudes (15 points)

B&B, p. 75 - #10,11,12 (Note: do you have to prove anything additional for 12 or just use logic?

2.2 Distances in a right triangle. (10 points)

B &B p. 101, #9, 10

2.3 Distances in a cube. (15 points)

B &B p. 101, #12, 13, 14, 15

2.4 More angle sums. (10 points)

(a) B & B, p. 87, #22.

2.5 Mean proportional. (10 points)

(a) B & B, p. 86, #14.

2.6 Dirichlet domains (10 points)

Given 3 points A, B and C, the plane can be divided into 3 regions, U(A), U(B), U(C), where U(A) for example is the set of all points which are closer to A than to B or C. Draw a random triangle and construct the 3 Dirichlet domains. Hint #1. Use last weeks problem on this topic as a tool. Hint #2. Read GTC, p. 37.

Return to Math 444 Home Page.