Geometry Midterm Reveiw
____ 1. ____ two points are collinear.
a. Any b. Sometimes c. No
____ 2. If find the values of x, EF, and FG. The drawing is not to
E F G
3. If Z is the midpoint of what are x, RZ, and RT?
R Z T
5 x - 22 53
4. and are complementary angles. m = , and m = . Find the
measure of each angle.
____ 5. Find the distance between points P(5, 4) and Q(3, 2) to the nearest tenth.
6. A high school soccer team is going to Columbus, Ohio to see a professional soccer game. A
coordinate grid is superimposed on a highway map of Ohio. The high school is at point (3, 4) and the
stadium in Columbus is at point (7, 1). The map shows a highway rest stop halfway between the
cities. What are the coordinates of the rest stop? What is the approximate distance between the high
school and the stadium? (One unit 4.3 miles.)
____ 7. What conjecture can you make about the product of 13 and 8,888,888?
88 = 1144
888 = 11,544
8888 = 115,544
88,888 = 1,155,544
____ 8. What is a counterexample for the conjecture?
Conjecture: The product of two positive numbers is greater than the sum of the two numbers.
____ 9. Another name for an if-then statement is a ____. Every conditional has two parts. The part following
if is the ____ , and the part following then is the ____.
____ 10. For the following true conditional statement, write the converse. If the converse is also true, combine
the statements as a biconditional.
If x = 5, then x2 = 25.
____ 11. Name the Property of Equality that justifies this statement:
If m = n, then .
____ 12. Complete the two-column proof.
____ 13. What is the value of x?
(7x – 2)°
(6x + 14)°
Drawing not to scale
____ 14. Write a two-column proof for:
Given: and are supplementary.
____ 15. Which two lines are parallel?
____ 16. What is an equation in point-slope form for the line perpendicular to y = 2x – 12 that contains (2, –4)?
____ 17. What other information do you need in order to prove the triangles congruent using the SAS
B C D
____ 18. What is the value of x?
Drawing not to scale
____ 19. is a perpendicular bisector to at between M and P. By which of the
five congruence statements, HL, AAS, ASA, SAS, and SSS, can you immediately conclude that
____ 20. Find the value of x.
2x – 9
____ 21. Q is equidistant from the sides of Find the value of x. The diagram is not to scale.
____ 22. Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was 131 ft
from camera 2, which was 145 ft from camera 3. Cameras 1 and 3 were 109 ft apart. Which camera
had to cover the greatest angle?
____ 23. If what is the relationship between
A B C
____ 24. In the parallelogram, and Find diagram is not to scale.
____ 25. For the parallelogram, if and find The diagram is not to scale.
26. In parallelogram DEFG, DH = x + 3, HF = 2y, GH = 3x – 1, and HE = 5y + 5. Find the values of x and y. The
diagram is not to scale.
____ 27. If and find the values of x and y for which
LMNO must be a parallelogram. The diagram is not to scale.
____ 28. What is the most precise name for quadrilateral ABCD with vertices A(–2, 2), B(0, 6), C(6, 6),
and D(4, 2)?
____ 29. Find the measure of the numbered angles in the rhombus. The diagram is not to scale.
____ 30. In rectangle PQRS, PR = 18x – 24 and QS = x + 146. Find the value of x and the length of
____ 31. What is the
value of x?
____ 32. Find the value of x for the figure at right M
____ 33. Find the geometric mean for 252 and 7
____ 34. Are the two triangles similar? How do you know?
C E F H
____ 35. Use the information in the diagram to determine the height of the tree to the nearest foot.
____ 36. Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48
feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes
were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the
flagpole to the nearest tenth of a foot.
____ 37. What is the value of x, given that ?
Find the length of the missing side. The triangle is not drawn to scale.
____ 39. Write the tangent ratios for and .
Not drawn to scale
Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth.
Not drawn to scale
____ 41. A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem
pole casts a 249-foot-long shadow. Find the measure of to the nearest degree.