MA 202-01
§10.1 – 10.5 Test #2 score
Name:
29 June 2001
1. Using only a compass and straight edge, construct each of the following. In some cases
you may need to add written instructions to explain the steps used in the construction if
they are not clear from your drawing. (4 points each)
(a) An equilateral triangle.
(b) A 75◦angle.
(c) Draw any line segment and divide it into three congruent parts.
(d) Draw 2 distinct parallel lines, l and m. Select any point P located between the lines.
Construct a circle that passes through P and is tangent to l and m. (You should come
up with a construction method that will work no matter how the point P is selected.)
(e) Draw any acute triangle. Construct a similar triangle whose sides are twice as long
as the original ones.
2. In each of the following, find xand y, if possible. Explain what you do, or why it is not
possible to find the value, as appropriate.
In the first figure, the line BC is parallel to DE, and in the second, xrepresents the length
of a side of the triangle, not the whole line you see in the figure. (4 points each)
x
y
10 12
8
A
B
DE
CA
B
C
D
E
4
6
x
3. For which of the following figures is it possible to construct a circle that circumscribes the
figure? Justify your answers. If a circumscribing circle does exist, exhibit the construction
in a particular example. (4 points each)
(a) a rectangle
(b) an isosceles trapezoid
(c) a rhombus that is not a square
4. Answer question 3 for an inscribed circle. (4 points each)
5. A girl wants to calculate the height of her family’s teepee. She is 112 cm tall and she finds
that when she is inside and stands so that her head touches the side, her feet are 64 cm
from the edge. If the teepee is a right circular cone with a diameter of 352 cm, what is its
height? (6 points)
