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° 1
l
2 3
4 5
7 m
6
MCPS – Geometry − January, 2003
1
, Geometry A final exam review KEY
5. Find the measures of the numbered angles. Use mathematics to explain the
BCR process you used to determine the measures. Use words, symbols, or both in your
explanation.
100°
m∠1 = _______
40°
m∠2 = _______
1 2 85°
140°
m∠3 = _______
40° 3 55°
m∠4 = _______
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 1
interior angles 2
9. Use the figure below and the given information to determine which lines are
BCR parallel. Use mathematics to explain the process you used to determine your
answer. Use words, symbols, or both in your explanation.
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
MCPS – Geometry − January, 2003
2
, 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
Provide a sketch. Label and give
the coordinates for the vertices of
A B 13 each rectangle.
-13 G E J
E (7, -1)
F (7, -9)
G (3, -1)
H (3, -9)
J (11, -1)
H F K 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
BCR process you used for your construction. Use words, symbols, or both in your
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
3
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° 1
l
2 3
4 5
7 m
6
MCPS – Geometry − January, 2003
1
, Geometry A final exam review KEY
5. Find the measures of the numbered angles. Use mathematics to explain the
BCR process you used to determine the measures. Use words, symbols, or both in your
explanation.
100°
m∠1 = _______
40°
m∠2 = _______
1 2 85°
140°
m∠3 = _______
40° 3 55°
m∠4 = _______
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 1
interior angles 2
9. Use the figure below and the given information to determine which lines are
BCR parallel. Use mathematics to explain the process you used to determine your
answer. Use words, symbols, or both in your explanation.
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
MCPS – Geometry − January, 2003
2
, 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
Provide a sketch. Label and give
the coordinates for the vertices of
A B 13 each rectangle.
-13 G E J
E (7, -1)
F (7, -9)
G (3, -1)
H (3, -9)
J (11, -1)
H F K 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
BCR process you used for your construction. Use words, symbols, or both in your
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
3
