Geometry

MATH 334, College Geometry Spring, 2015 Assignment No. 8 Sections 5.1-5.3

Instructions: Complete the following problems on separate sheets of paper. Your work must be organized and must follow a logical process. Correct use of notation and symbols as adopted in class is required. Proofs must be accompanied by figures.

Work each problem in Euclidean Geometry.

1. In the figure to the right, ⇤ABEF and ⇤DEFG are parallelograms and point C is the intersection of BE and DG. If µ(\EFG) = 68o, µ(\CEF) = 60

o

, and µ(\BDC) = 25o, find the measures of \DGF , \CED, \BCG, \GAB, \EDG, and \AGF .

A B

C D

E F

G

2. Let ⇤ABCD be a trapezoid with AB || CD. Prove that if AD ⇠= BD, then \DAB ⇠= \ABC.

3. Prove Clairaut’s Axiom.

4. Prove that the diagonals of a kite

(a) bisect each other.

(b) intersect at right angles.

5. In each figure below, give a statement for two similar triangles, state why they are similar, and find requested measurements.

(a) Find CD and AE if ! BD ||

! AE.

A

B

C

D

E

4

8

8

8

(b) Find FH and GH if \FGH ⇠= \IFH.

F

G

H

I

14

9

4

(c) Find KL and JN if \KJN ⇠= \KML.

J

K

L

M

N

3

8 7.5

4.5

6. Let ⇤ABCD be any convex quadrilateral. If E, F , G, and H are the midpoints of sides AB, BC, CD, and AD, respectively, then ⇤EFGH is a parallelogram. Hint: Draw diagonal AC, then show �ABC ⇠ �EBF .