Elementary_Geometry_exam.pdf

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GEOMETRY A
Geometry A final exam review KEY
GEOMETRY A
NAME _______ KEY ___________
FINAL EXAM REVIEW
UNIT I: INTRODUCTION TO GEOMETRY
1.
Name the three undefined terms of geometry.
Point, line, and plane
2.
Given the diagram of a right hexagonal prism, determine whether each statement
is true or false.
B
C
a.
A, B, and C are collinear.
False
A
D
b.
D, E, K, and J are coplanar. True
F
E
c.
B and J are collinear.
True
H
I
d.
E, F, J, and K are coplanar. False
G
J
L
K
3.
Xena lives 15 blocks from Yolanda and Yolanda lives 5 blocks from Zuri. Given
all three houses are collinear, which one of the following locations of points is
NOT possible ?
A.
X
Y
Z
B.
X
Z
Y
C.
Y
X
Z
4.
Name all the angles with a measure of 110°.
∠∠∠
3, 4, 7
l || m
110°
3
1
l
2
4
5
m
6
7
MCPS – Geometry − January, 2003
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Geometry A final exam review KEY
5.
Find the measures of the numbered angles. Use mathematics to explain the
process you used to determine the measures. Use words, symbols, or both in your
BCR
explanation.
m∠1 = _______
100 °
1
2
85°
m∠2 = _______
40 °
m∠3 = _______
140 °
40°
3
m∠4 = _______
55 °
4
6.
Complete the following statements.
a. The ceiling and the floor of our classroom are examples of parallel planes.
b. The wall and the floor of our classroom are examples of perpendicular planes.
7.
Two lines that do not lie in the same plane are called skew lines.
8.
Make a sketch that illustrates a pair of alternate interior angles.
∠ 1 and ∠ 2 are alternate
interior angles
1
2
9.
Use the figure below and the given information to determine which lines are
parallel. Use mathematics to explain the process you used to determine your
answer. Use words, symbols, or both in your explanation.
BCR
m∠3 + m∠5 = 180°
2
r
1
3
4
5
s
6
a
b
Parallel lines:
r || s
10. Name the solid of revolution formed when the given figure is rotated about the
line.
a.
b.
c.
d.
Cone
Cylinder
Sphere
Torus or Donut shape
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Geometry A final exam review KEY
11. If EF is congruent to AB , then how many rectangles with EF as a side can be
drawn congruent to rectangle ABCD? _____ 2 _______
6
D
C
-13
A
B
13
Provide a sketch. Label and give
the coordinates for the vertices of
each rectangle.
G
E
J
H
F
K
E (7, -1)
F (7, -9)
G (3, -1)
H (3, -9)
J (11, -1)
K (11, -9)
-10
12.
If a plane were to intersect a cone, which of the following could NOT represent
the intersection?
____________
A. Circle
B. Rectangle
C. Ellipse D. Line E. Point
13.
If a plane were to intersect a cylinder, which of the following could NOT
represent the intersection? ____________
A. Circle
B. Rectangle
C. Trapezoid D. Line E. Point
14.
Construct an equilateral triangle with a median. Use mathematics to explain the
process you used for your construction. Use words, symbols, or both in your
BCR
explanation.
15H. Construct the inscribed circle and the circumscribed circle for a scalene triangle.
ECR Use mathematics to explain the process you used for your construction. Use
words, symbols, or both in your explanation.
Student needs to construct perpendicular bisectors of the sides of the triangle to find
the center of the circumscribed circle (this center is equidistant from the vertices of the
triangle) and needs to construct angle bisectors of the triangle to find the center of the
inscribed circle (this center is equidistant from the sides of the triangle.) Students
should then draw the appropriate circle.
MCPS – Geometry − January, 2003
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Geometry A final exam review KEY
16.
Construct a pair of parallel lines. Use mathematics to explain the process you used
for your construction. Use words, symbols, or both in your explanation.
BCR
A sample solution is provided here.
There are other representations.
17.
Using the angles and segment below, construct triangle ABC. Use mathematics to
explain the process you used for your construction. Use words, symbols, or
both in your explanation.
BCR
B
C A sample solution is provided here.
There are other representations.
A
A B
A
B
18. Construct DC as the perpendicular bisector of AB . Use mathematics to explain
the process you used for your construction. Use words, symbols, or both in your
explanation.
BCR
D
D C
A
B
C
19.
The crew team wants to walk from their boat house to the nearest river. Show by
construction which river is closest to the boat house. Construct the shortest path
to that river. Use mathematics to explain the process you used to determine your
answer. Use words, symbols, or both in your explanation.
ECR
Allegheny River
Ohio River
•
Boat house
•
Monongahela River
MCPS – Geometry − January, 2003
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Geometry A final exam review KEY
20.
A civil engineer wishes to build a road passing through point A and parallel to
Great Seneca Highway. Construct a road that could meet these conditions. Use
BCR
mathematics to explain the process you used for your construction. Use words,
symbols, or both in your explanation.
• A
Great Seneca Highway
21.
If Wisconsin Avenue is parallel to Connecticut Avenue and Connecticut Avenue
is parallel to Georgia Avenue, then what relationship exists between Wisconsin
Avenue and Georgia Avenue? They are parallel (Provide a sketch.)
Wisconsin Ave.
Connecticut Ave.
Georgia Ave.
22.
Using a flow chart, paragraph , or two-column proof, prove why any point P on
the perpendicular bisector of AB is equidistant from both points A and B.
Student’s proof should indicate choosing a point on the
perpendicular bisector, not on segment AB, and proving
congruent triangles.
ECR
P
A
B
23.
Sketch and describe the locus of points in a plane equidistant from two fixed
points. The locus is the perpendicular bisector of the segment that connects
those two points.
24.
Sketch and describe the locus of points on a football field that are equidistant
from the two goal lines. The locus is the 50 yard line on the football field.
locus
26.
Can you construct a 45° angle with only a compass and straight edge. Use
mathematics to explain the process you could use to construct the angle. Use
words, symbols, or both in your explanation . Yes. Construct two perpendicular
lines. Then construct an angle bisector of one of the right angles formed by the
two perpendicular lines.
ECR
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