Download Geometry

Geometry
Practice End-of-Course Exam #2
Name _________________________
Teacher _____________
Per ___________
1
Given line PM, the drawing shows the beginning steps of a geometric construction.
Which construction is shown?
����� .
Ο A. The perpendicular bisector of 𝑃𝑀
Ο B. The line parallel to line PM through point P.
Ο C. A line perpendicular to line PM at point M.
Ο D. A line perpendicular to line PM at point P.
2
Look at the diagram.
5x-9
A
Ο A. 11°
Ο B. 64°
Ο C. 68°
Ο D. 88.28°
6x+2
2x
Determine the m ∠ BCD.
B
C
D
3
Three vertices of a triangle are F(0,7), G(3, 1), and H(0, 1).
You may use the blank grid to help determine the solution.
•
Determine the coordinates of the point C that is equidistant from the vertices of
the triangle.
Write your answer on the line.
What are the coordinates of the point C? ( _____ , _____ )
•
Determine the distance from point C to any of the vertices. Round your answer to
two decimal places.
Write your answer on the line.
What is the distance from point C to any of the vertices? __________
4
Triangle JKE is an obtuse isosceles triangle with m∠E = 10 and KE > JK.
What is the m∠J?
Ο A. 170
Ο B. 16
Ο C. 85
Ο D. 10
5
Look at the diagram.
K
M
L
N
J
What theorem or postulate can you use to prove ∆𝐾𝐿𝑀 ≅ ∆𝑁𝐿𝐽?
Ο A. Corresponding Parts of Congruent Triangles are Congruent
Ο B. Side-Angle-Side Congruence
Ο C. Angle-Side-Angle Congruence
Ο D. Side-Side-Side Congruence
6
Look at the diagram.
B
A
E
C
D
Which theorem or postulate can you use to prove ∆𝐸𝐵𝐶 ≅ ∆𝐸𝐷𝐴?
Ο A. Angle-Angle-Side Congruence
Ο B. Side-Angle-Side Congruence
Ο C. Corresponding Parts of Congruent Triangles are Congruent
Ο D. Side-Side-Side Congruence
7
A proof is shown.
Fill in the blanks for steps 5 and 6 to complete the proof.
Given: B is the midpoint of ����
𝐴𝐸 .
����
B is the midpoint of 𝐶𝐷.
Prove: ∆𝐴𝐵𝐷 ≅ ∆𝐸𝐵𝐶.
A
C
B
D
E
Statements
1. B is the midpoint of ����
𝐴𝐸 .
8
Reasons
1. Given
���� ≅ 𝐵𝐸
����
2. 𝐴𝐵
2. Definition of midpoint
���� ≅ ����
4. 𝐶𝐵
𝐵𝐷
4. Definition of midpoint
3. B is the midpoint of ����
𝐶𝐷.
3. Given
5.
5. Vertical Angles Theorem
6. ∆𝐴𝐵𝐷 ≅ ∆𝐸𝐵𝐶
6.
One leg of a 45° − 45° − 90° triangle is 8 cm long.
Determine the length of the hypotenuse.
Ο A. 8√3
Ο B. 8√2
Ο C. 4√2
Ο D. 16
9
Cody is standing 14 feet from the base of the tree. The top of the tree makes a 60° angle
with the ground at the point where he is standing.
60°
14 ft
Determine the height of the tree. Round your answer to two decimal places.
Write your answer on the line.
What is the height of the tree? _________ feet
10
The diagonal of a square is 7 cm.
7 cm
Determine the length of one side of the square.
1
Ο A. 3 2
Ο B. 7√2
Ο C.
7√3
Ο D.
7√2
3
2
11
Look at the triangle.
18
13
5
y
Determine the length of y. Express your answer in simplified radical form.
Write your answer on the line.
What is the length of y? _________
12
A triangle has side lengths of 6, 7, and 11 inches. Which statement is true?
Ο A. The triangle is an acute triangle.
Ο B. The triangle is a right triangle.
Ο C. The triangle is an obtuse triangle.
Ο D. The side lengths cannot form a triangle.
13
Which statement is true about all parallelograms?
Ο A. The diagonals bisect pairs of opposite angles.
Ο B. The diagonals are congruent.
Ο C. The diagonals bisect each other.
Ο D. The diagonals are perpendicular.
14
Look at the diagram.
(6𝑎 − 7)°
𝑏°
(4𝑎 + 20)°
Determine the values for a and b that would make the quadrilateral a parallelogram.
Ο A. a = 13.5, b = 166.5
Ο B. a = 16.7, b = 93.2
Ο C. a = 13.5, b = 106
Ο D. a = 16.7, b = 86.8
15
Quadrilateral MNOP is a rectangle. 𝑀𝑂 = 16.
N
O
Q
P
M
���� .
Determine the length of 𝑃𝑄
Write your answer on the line.
����? _________
What is the length of 𝑷𝑸
16
Quadrilateral ABCD is a rhombus and m∠BCE = 50°.
A
B
E
C
D
Determine the m∠EBC.
Write your answer on the line.
What is the m∠EBC? _________ °
17
Quadrilateral EFGH is an isosceles trapezoid.
F
E
Determine the measure of angle F.
Ο A. 155.5°
Ο B. 131°
Ο C. 103.7°
Ο D. 49°
G
49°
H
18
An exterior angle measure of a regular polygon is 12°.
Which of the statements is true?
Ο A. The polygon has 15 sides and the measure of each interior angle is 168°.
Ο B. The polygon has 30 sides and the measure of each interior angle is 168°.
Ο C. The polygon has 15 sides and the measure of each interior angle is 156°.
Ο D. The polygon has 28 sides and the measure of each interior angle is 167°.
19
Three vertices of a square have coordinates (3, 1), (4, -4) and (-1, -5). The diagonals of
the square intersect at point Q.
Determine the coordinates of point Q.
You may use the blank grid to help determine the solution.
Write your answer on the line.
What are the coordinates of point Q? ( _____ , _____ )
20
The diagram shows a section of the support structure of a roller coaster.
In parallelogram JKLM, JK = (3z – 0.9) feet and LM = (z + 2.7) feet.
•
•
Determine the length of JK.
Explain your reasoning. Include which property or properties of parallelograms
you used to solve the problem.
What is the length of JK? _________ feet