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Geometry Midterm Review Spring 2011 Page 1 of 18 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 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

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Page 1: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 1 of 18

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.

Page 2: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 2 of 18

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.

Page 3: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 3 of 18

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. ____________

Page 4: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 4 of 18

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: ______________________

Page 5: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 5 of 18

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) _____________________________________

Page 6: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 6 of 18

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. _________

Page 7: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 7 of 18

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. ______________

Page 8: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 8 of 18

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. _______

Page 9: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 9 of 18

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. ________

Page 10: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 10 of 18

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. _______________

Page 11: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 11 of 18

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. _______

Page 12: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 12 of 18

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. ________

Page 13: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 13 of 18

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. ________

Page 14: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 14 of 18

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

Page 15: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 15 of 18

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. ________________

Page 16: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 16 of 18

Solve for the indicated variable.

41. 42. 41. ________

42. ________

43. 44. 43. ________

44. ________

45. 46. 45. ________

46. ________

47. 48. 47. ________

48. ________

Page 17: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 17 of 18

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

_____________ _____________ _____________ ______________

Page 18: Geometry Midterm Review 033011 · Geometry Midterm Review Spring 2011 Page 2 of 18 Use a protractor to find the measure of the given angle. Then classify the angle as acute, obtuse,

Geometry Midterm Review Spring 2011

Page 18 of 18

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