Winter 2009 MATH 330B/539 Geometry Homework 1 Hints

Assigned Homework Set #1

Hints for assigned problems:

For #3(a) start by showing that triangle(AOD) ~ triangle(COB). For #3(b), draw a very lopsided trapezoid.
Do suggested problem #14 before trying assigned problem #15. For #15, let square #1 be square(ABCD), labeled as follows. Label the lower left corner of the square as point A. Proceeding counterclockwise, label the other corners B, C, and D. Draw square #2 by connecting the midpoints of the sides of square #1. Draw the square #3 by connecting the midpoints of the sides of square #2, etc. Label the midpoints as follows. Let M1 be the midpoint of side AB. Let M2 be the midpoint of the first side of square #2. (The side of square #2 that you are on when you go counterclockwise from point M1.) Let M3 be the midpoint of the first side of square #3. (The side of square #3 that you are on when you go counterclockwise from point M2.), etc. Let x = length of side AB.
Notice that #16 has a picture on the next page.

Suggested Problems:

Hints for suggested problems:

For #9(a) first show that area(triangle(ADC)) = area(triangle(ABC)).
For #9(b) first show that triangle AFD ~ triangle BEA.
For #11, let h = the height to side AC and let b = length of side BC. Do the problem two ways:
1. Without similarity: set up an equation by setting area of whole triangle = area of sum of parts. Solve this equation.
2. With similarity: Show that triangle(BEF) ~ triangle(BAC) and then use that result.
For #14 let x = AB = length of one side of triangle(ABC). Determine length M1M2 in terms of x. Then determine length M2M3 in terms of x, etc.

Last updated March 8, 2009.