Name:
Math 362 - Section 001
Winter 2004
Practice Test 1
Closed Book / Closed Note. Write your answers on the test itself. Answer all 10 problems.
1.
A model for Axioms I-1 and I-2 has points S = {1, 2, 3, 4} and lines {1, 2}, {1, 3},
{1, 4}, and {2, 3}.
a.
What sets must the remaining lines be?
{2, 4} and {3, 4}
b.
What sets must the planes be?
{1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}
2.
Consider the model: Points: S= { 1, 2, 3, 4, 5}; Lines: {1, 2, 3, 4}, {1, 5}, {2, 5}, {3, 5},
{4, 5}, {3,4}; and Planes: {1, 4, 5}, {2, 4, 5}, {2, 3, 4}.
a.
Does the model satisfy axiom I-2 (“A plane is determined by three noncollinear
points.”)?
NO. ({1, 2, 5}, {1, 3, 5}, {2, 3, 5}, {3, 4,5 } are all missing.)
b.
Does the model satisfy axiom I-3 (“A line passing through two points of a plane
lies in that plane.”)?
NO. (The line {1, 2, 3,4} passes through
3.
Suppose that in a geometry satisfying axioms D-1 – D-3, points A, B, C and D are
collinear, and AB=AC = 3, BC = 6, BD = 2, CD = 4, and AD = 2. What betweeness
relations follow by definition among these four points?
B-A-C and B-D-C
4.
Suppose that K[3], L[5], and W[x] are three points lying on a line, with their coordinates
as given. If KW =5 and LW = 7, what are the possible values for x?
Only -2
5.
Rays on one side of
opposite ray
the figure, find
a.
have their coordinates as indicated in the figure. Ray
, and
is opposite
is
. Using the betweeness relations evident in
mpABG
47
b.
mpGBD
165
6.
If ray
the line
has coordinate 0 in a coordinate system with respect to the rays on one side of
, mpRST = 72, and
coordinate of ray
, what are the possible values for the
?
162 or possibly 18 on the other side of the half-plane.
7.
Two lines
meet at a point M, with A-M-B and C-M-D. Identify the shaded region
in the figure in terms of half-planes.
(You could also use point M to
identify lines, as in:
8.
Use half-plane notation to identify the interior of ªABC, as indicated in the figure.
(I asked the wrong
question here, but. . . )
9.
Point B lies on
and you are given that mpABC = 40 and mpABE = 160. In addition,
the ray opposite ray
10.
bisects pABC. What values are possible for mpDBE? Only 20.
Consider the following relationships among three angles: p1 is complementary to p2, p1
is supplementary to p3, and the sum of the measures of p2 and p3 equalts 120. Find
mp2.
mp2 = 15