Geometry Midterm Review Spring 2011
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Name_______________________________ Date_____________ Period______
Unit 1
1. Give two other names for AB����
. 1. _____________
2. Name three points that are collinear. 2. _____________
3. Name a pair of opposite rays. 3. _____________
4. Give another name for CD����
. 4. _____________
Point J is between H and K on HK . Use the given information to write an equation in terms of x. Solve
the equation. Then find HJ and JK.
5. _____________
6. _____________
7. _____________
8. _____________
Find the distance between the points. Leave answer in simplest radical form.
9. 10. 9. _____________
10. _____________
The endpoints of two segments are given. Find each segment length. Tell whether the segments are
congruent.
11. 12. 11. _____________
_____________
12. _____________
_____________
5.
7.
6.
8.
Geometry Midterm Review Spring 2011
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Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse, right, or
straight.
13. AFB� 14. BFD� 13. ____________
14. ____________
15. AFC� 16. AFE� 15. ____________
16. ____________
Roof trusses can have several different layouts. The diagram below shows one type of roof truss made out
of beams of wood. Use the diagram to identify two different examples of the indicated type of angle pair.
In the diagram HBC� and BCE� are right angles.
17. Supplementary angles 17. ____________
18. Complementary angles 18. ____________
19. Vertical angles 19. ____________
20. Linear pair angles 20. ____________
Tell whether the figure is a polygon. If it is not, explain why. If it is a polygon, tell whether it is convex or
concave.
21. 22. 21. ____________
22. ____________
23. 24. 23. ____________
24. ____________
25. The perimeter of a rectangle is 690 inches and its length is 213 inches. 25. ____________
Find the width of the rectangle.
Geometry Midterm Review Spring 2011
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26. You are planting grass on a square plot of land. You are also building a fence around the edge of the
plot. The side length of the plot is 54 yards.
a. How much area do you need to cover with grass seed? 26a. ___________
b. How many feet of fencing do you need? 26b. ___________
27. You make a window out of a rectangular pane of
glass by surrounding it with a wooden frame that
is x inches wide. The pane of glass is 20 inches
long and 24 inches wide. The perimeter of the
window is 2
38 feet. What is the value of x. 27. ____________
28. Find the circumference of the circle. 28. ____________
Round your answer to the nearest tenth.
Use the diagram below. Tell whether the angles are vertical angles, a linear pair, or neither.
29. 1� and 2� 30. 1� and 3� 29. ____________
30. ____________
31. 2� and 4� 32. 3� and 4� 31. ____________
32. ____________
Geometry Midterm Review Spring 2011
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Solve for the values of x and y.
33. 34. 33. x = ____ y = ____
34. x = ____ y = ____
35. 36. 35. x = ____ y = ____
36. x = ____ y = ____
Unit 2
Draw the next figure in the pattern.
1. 2.
_____________ _____________
The first three objects in a pattern are shown. How many gray squares are in the next object?
3. 4. 3. ___________
4. ___________
Write the next number in the pattern. Describe the pattern in the numbers.
5. 113, 224, 335, 446, _____ 6. 4, 6, 9, 13, 18, _____
pattern: ______________________ pattern: ______________________
7. 1, 4, 9, 16, _____ 8. 2, 5, 11, 23, _____
pattern: ______________________ pattern: ______________________
Geometry Midterm Review Spring 2011
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Rewrite the given statements below in conditional (if-then) form. Underline the hypothesis, and circle the
conclusion.
9. It is time for dinner if it is 6 p. m. ______________________________________________
10. There are 12 eggs if the carton is full. _____________________________________________
11. An obtuse angle is an angle that measures more that 90° and less than 180°.
________________________________________________________________
12. The car runs when there is gas in the tank. ____________________________________________
Write the converse, inverse, and contrapositive of each statement below:
13. If you like hockey, then you go to the hockey game.
Converse: _________________________________________________
Inverse: ___________________________________________________
Contrapositive: _________________________________________________
14. If x is odd, then 3x is odd.
Converse: _________________________________________________
Inverse: ___________________________________________________
Contrapositive: _________________________________________________
Write the converse of each true statement. If the converse is also true, combine the statements to write a
true bi-conditional statement.
15. If an angle measures 30°, then it is acute.
Converse: ________________________________
Bi-conditional (if applicable) _____________________________________
16. If two angles are supplementary, then their sum if 180°.
Converse: ________________________________
Bi-conditional (if applicable) _____________________________________
Geometry Midterm Review Spring 2011
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True or False
17. Three noncollinear points determine a plane. 17. ______
18. Any three points lie on a distinct line. 18. ______
19. Through any two points, there exists exactly one line. 19. ______
20. A line contains at least two points. 20. ______
Write the property that completes the statement.
21. 21. ________________
22. 22. ________________
23. 23. ________________
24. 24. ________________
Use the diagram at the right to solve for the indicated angles. Label the angle measure.
25. 25. ________________
26. 26. ________________
27. 27. ________________
28. 28. ________________
Solve for x.
29. W Z≅� � 30. FG JH= 29. _________
30. _________
Geometry Midterm Review Spring 2011
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Solve for x.
31. 32. 31. ______
32. ______
Unit 3
Think of each segment in the diagram as part of a line. Complete the statement with parallel, skew, or
perpendicular.
1. 1. ______________
2. 2. ______________
3. 3. ______________
4. 4. ______________
Classify the following angles as corresponding, alternate interior, alternate exterior, consecutive (same
side) interior, or no relation.
5. 5. ______________
6. 6. ______________
7. 7. ______________
8. 8. ______________
9. 9. ______________
10. 10. ______________
11. 3∠ and 13∠ 11. ______________
12. 3∠ and 8∠ 12. ______________
Geometry Midterm Review Spring 2011
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Find the value of x that makes //m n .
13. 14. 13. ________
14. ________
15. 16. 15. ________
16. ________
Find the slope of the line that passes through the given points.
17. (1, 2) and (7, 7) 18. (3, 4) and (-5, 0) 17. ________
18. ________
19. (5, -2) and (5, 8) 20. (3, 1) and (-5, 3) 19. ________
20. ________
Identify the slope of the line that would be parallel to the given line.
21. 5 3y x= − 22. 4 2 4x y− + = 23. 5 3( 2)y x− = − 21. _______
22. _______
23. _______
Identify the slope of the line that would be perpendicular to the given line.
24. 2 3y x= + 25. 3 8x y− = 26. 2 5( 6)y x+ = − 24. _______
25. _______
26. _______
Geometry Midterm Review Spring 2011
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Determine which of the following lines, if any, are parallel or perpendicular.
27. 27. ______________________
28. 28. ______________________
Write an equation of the line that passes through the given points.
29. (-1, 0), (0, -2) 30. (0, 4), (6, 13) 29. _______________
30. _______________
31. (4, 5), (8, 2) 32. (-1, -9), (6, 5) 31. _______________
32. _______________
Find the measures of the following angles:
33. 3� 34. 4� 35. 5� 36. 6� 33. ________
34. ________
35. ________
36. ________
Geometry Midterm Review Spring 2011
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Graph each equation.
37. 38. 39.
40.
Unit 4
Find the values of the missing variables.
1. 2. 1. _______________
2. _______________
3. 4. 3. _______________
4. _______________
5. 6. 7. 5. _______________
6. _______________
7. _______________
Geometry Midterm Review Spring 2011
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Find the values of the variables.
8. 9. 8. _____________
9. _____________
10. 11. Find the perimeter of the triangle. 10. _____________
11. P = _________
12. In ∆DEF if DE EF≅ and m ∠ D is 43, then m ∠ F is ? . 12. __________
13. In ∆XYZ if XY YZ≅ and m ∠ Y = 52, then m ∠ Z is ?_. 13. __________
14. In ∆DOG if ∠ O ≅ ∠ G, DO = 2x + 3, OG = 2x, and DG = 9, then x is _?_. 14. __________
15. In ∆CAT if ∠ C ≅ ∠ A, CA = 7, and AT = 4, then CT is _?_. 15. __________
If TJM PHS∆ ≅ ∆ , then…
16. P ≅� __?__ 16. _______
17. JM ≅ __?__ 17. _______
18. MT = __?__ 18. _______
19. HPS∆ ≅ __?__ 19. _______
Geometry Midterm Review Spring 2011
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Is the given information enough to prove the triangles congruent? If so, write a congruence
statement and state the theorem or postulate to justify your reasoning.
20. 21. 22. 23.
20. Yes or No 21. Yes or No 22. Yes or No 23. Yes or No
∆ABD ≅ _______ ∆STR ≅ _______ ∆MAE ≅ _______ ∆ADK ≅ _______
State the third congruence that is needed to prove that DEF QRT∆ ≅ ∆ using the given postulate or
theorem.
24. Given that , ,D Q F T≅ ≅� � � � then _________ ≅ _________ by the AAS Congruence Theorem.
25. Given that , ,E R EF RT≅ ≅� � , then _________ ≅ _________ by the ASA Congruence Theorem.
26. Given that , ,DE QR D Q≅ ≅� � then _________ ≅ _________ by the SAS Congruence Theorem.
27. Given that , ,DE QR FD TQ≅ ≅ then _________ ≅ _________ by the SSS Congruence Theorem.
Unit 5
Given BD is the perpendicular bisector of AC and 52m A = °� ,…
1. Classify the triangle. 1. ______________
2. Solve for x. 2. ________
3. Solve for m C� . 3. ________
4. Solve for m CBA� . 4. ________
Geometry Midterm Review Spring 2011
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C
D
A B
Is it possible to construct a triangle with the given side lengths? If not, explain
why not.
5. 3, 4, 5 5. Y or N __________________
6. 1, 4, 6 6. Y or N __________________
7. 17, 17, 33 7. Y or N _________________
8. 22, 26, 65 8. Y or N __________________
Describe the possible lengths of the third side of the triangle given the lengths
of the other two sides.
9. 6 inches, 9 inches 9. _________________
10. 4 feet, 12 feet 10. _________________
11. 9 meters, 18 meters 11. _________________
12. 21 yards, 16 yards 12. _________________
In each of the following triangles tell whether BD is a perpendicular bisector, angle bisector, median, or
altitude. List all that apply.
13. 14. 13. ___________________________
14. ___________________________
15. 16. 15. ___________________________
16. ___________________________
Solve for the indicated variable given the proportion.
17. 18. 19. 20. 17. ________
18. ________
19. ________
20. ________
Geometry Midterm Review Spring 2011
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Given similar polygons,...
21. …corresponding angles are __?__ 21. _______________
22. …corresponding sides are __?__ 22. _______________
23. …corresponding perimeters are __?__ 23. _______________
24. Corresponding parts can be determined by __?__ 24. _______________
The polygons below are similar as indicated. Find the value of x.
25. 26. 25. ________
26. ________
27. A rectangle has a length of 6 meters. A similar rectangle is drawn using a scale 27. ________
of 1:4. What is the length of the second rectangle?
28. You have two equilateral triangles. The scale factor is 3:2. The side length of 28. ________
the first triangle is 6 centimeters. What is the side length of the second triangle?
In the diagram, XYZ MNP∆ ∆∼ .
29. 29. _______
30. 30. ______, ______
31. 31. _______
32. 32. _______
D E
Geometry Midterm Review Spring 2011
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The two triangles are similar. Find the values of the variables.
33. 33. _____________
34. 34. _____________
35. Given ABC PQR∆ ∆∼ , solve for x. 36. Given RST XYZ∆ ∆∼ , solve for a.
35. _______
36. _______
Determine whether there is enough information to determine triangles similar.
If so, by what postulate?
37. 38. 37. _________________
38. _________________
39. 40. 39. ________________
40. ________________
Geometry Midterm Review Spring 2011
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Solve for the indicated variable.
41. 42. 41. ________
42. ________
43. 44. 43. ________
44. ________
45. 46. 45. ________
46. ________
47. 48. 47. ________
48. ________
Geometry Midterm Review Spring 2011
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13 18
x
12
x
13
9.5
3.1
x
8.x
4.
Solve for the indicated variable
49. 50. 49. ________
50. ________
51. 52. 51. ________
52. ________
Unit 6
Find the indicated variable. Figures are not drawn to scale. Round your answers to the nearest tenth.
1. 2. 1. ________
2. ________
3. 4. 3. ________
4. ________
Decide whether the numbers can represent the side lengths of a triangle. If they
can, classify the triangle as acute, right, or obtuse. Be sure to show your work.
5. 5, 7, 9 6. 8, 9, 10 7. 10, 12, 30 8. 16, 30, 34
_____________ _____________ _____________ ______________
Geometry Midterm Review Spring 2011
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30°
10
45° 30°
5 3
x y
Find the missing side lengths in the following triangles:
9. 10. 9. _________________
10. ________________
11. 12. 11. ________________
12. ________________
13. 13. ________________
60°
3 in.
x
y
x
y
45°
7
12
x
y
x y