Geometry Midterm Exam Practice Chapters 1 – 4 Name:

These problems serve as a representative sample of concepts that will be tested on the midterm exam. They

are core homework problems completed throughout the semester. This is NOT a comprehensive list so it is

important to also look over questions from chapter note guides. You will need to complete your work on a

separate sheet of paper!

Chapter 1

1-6. Simplify the expressions below as much as possible. Show every step.

a. 2a + 4(7 + 5a) b. 4(3x + 2) – 5(7x + 5)

1-29. Evaluate each expression below if a = -2 and b = 3.

a. 3a2 - 5b + 8 b. 2

3 b – 5a c.

𝑎+2𝑏

4 + 4a

1-35. Examine the rectangle at the right.

a. What is the perimeter in terms of x? In other

words, find the perimeter.

b. If the perimeter is 78 cm, find the dimensions of the rectangle. Show all your work.

1-44. Angela had a rectangular piece of paper and then cut a

rectangle out of a corner as shown at right. Find the

area and perimeter of the resulting shape.

1-97. Find the result when each indicated transformation is performed on the graphs below.

a. Reflect Figure A across line l. b. Rotate Figure B 90o clockwise about point P.

c. Reflect Figure C across line m. d. Rotate Figure D 180o about point Q.

1-116. Refer to ABC below.

a. Rotate ABC 90o counterclockwise about the origin to

create A’B’C’.

Name the coordinates of C’.

b. Reflect ABC across the vertical line x = 1 to create

A’’B’’C’’.

Name the coordinates of the vertices.

c. Translate ABC so that A’’’ is at (4, -5). Name the

coordinates of B’’’.

1-125. Without referring to your Shapes Toolkit, see if you can

recall the names of each of the shapes below. Then check your

answers with definitions from you Shapes Toolkit. How did you do?

1-127. Throughout this book, key problems have been selected as “checkpoints.” This problem is a checkpoint

for solving linear equations. It will be referred to as Checkpoint 1.

c. – 2x – 6 = 2 – 4x – (x – 1) d. 3x – 4 + 1 = – 2x + 5 + 5x

Chapter 2

*substitution *elimination

Chapter 3

3-8. On graph paper, graph line if

M(−1, 1) and U(4, 5).

a. Find the slope of and write an equation for the line.

b. Find MU (the distance from M to U).

3-9. Examine each diagram below. Identify the error in each

diagram.

3-18. Use the method from problem 3-2 to enlarge the shape

below from the origin by a zoom factor of 4.

3-34. Examine the diagram below. Name the geometric

relationships of the angles below.

d and e __________________________________

e and h __________________________________

a and e __________________________________

c and d __________________________________

3-65. Solve for the missing lengths in the sets of similar figures below. You may want to set up proportions to

help you write equations.

a. ABCD ∼ JKLM

b. ΔNOP ∼ ∆XYZ

3-78. Use the relationships in each diagram below to solve for x. Justify your solution by stating which

geometry relationships you used.

a. b.

3-90. Determine which of the following pairs of triangles are similar (AA, SAS, SSS) Explain your work.

a. b. c.

3-91. The dashed line below represents the line of symmetry of the shaded figure. Find

the area and perimeter of the shaded region. Show all work.

3-109. The area of the triangle below is 25 square units.

Find the value of h. Then find the perimeter of the entire triangle.

Show all work.

3-111. This problem is a checkpoint for writing linear equations from multiple representations.

It will be referred to as Checkpoint 3.

Write a linear equation that represents each situation.

a. An equation for the line at the right.

b. An equation for a line perpendicular to the line at right

and passing through the point (−1, −3). *Choose slope then plug in x & y!

c. An equation of the line passing through the points (4, 3) and (−1, 1).

*Find slope using formula then plug in x & y to solve for b!

Chapter 4

4-7. Use the triangles below to answer the following questions. Are the triangles at right similar?

a. How do you know? Show your reasoning in a flowchart.

b. Examine your work from part (a). Are the triangles also congruent? Explain why or why not.

4-17. Use your Trig Table Toolkit from problem 4-16 to help you find the value of each variable below.

a. = x =

4-20. Find the area and perimeter of the triangle below.

4-39. Find the missing side length for each triangle. Label the opposite and adjacent side. Use the tangent button on your calculator to help.

a. b.

4-43. When she was younger, Mary had to look up at a 68° angle to see into her father’s eyes whenever she was standing 15 inches away. How high above the flat ground were her father’s eyes if Mary’s eyes were 32 inches above the ground? Draw a diagram to support your answer.

4-74. Find x and y in the diagram below. Show all of the steps leading to your answer.

4-95. Use an area model, a tree diagram, or refer to the table you created in problem 4-10 that represents the sample space for the sum of the numbers when rolling two standard six-sided dice.

a. In a standard casino dice game the roller wins on the first roll if he rolls a sum of 7 or 11. What is the probability of winning on the first roll?

b. The player loses on the first roll if he rolls a sum of 2, 3, or 12. What is the probability of losing on the first roll?

c. If the player rolls any other sum, he continues to roll the dice until the first sum he rolled comes up again or until he rolls a 7, whichever happens sooner. What is the probability that the game continues after the first roll?