Name: ______________________ Class: _________________ Date: _________ ID: A

1

Geometry Semester 1 REVIEW

1. The figure below is a rectangular shipping box. Name two different planes that contain BC→←⎯⎯

.

2. Find BC.

3. The endpoints of GH are G −6,−9ÊËÁÁ

ˆ¯̃̃ and H 8,−7Ê

ËÁÁˆ¯̃̃. Find the coordinates of the midpoint M.

4. Find the area of FGH with coordinates F −4,−6ÊËÁÁ

ˆ¯̃̃,G 1,3Ê

ËÁÁˆ¯̃̃, and H 2,−6Ê

ËÁÁˆ¯̃̃.

ID: A

2

5. Find m∠BDC.

6. A ramp that is used to load a truck makes supplementary angles with the ground. The ramp has an incline (∠1) of 25°. What is the measure of ∠2?

7. Let p be “an animal is a dog” and let q be “an animal is a golden retriever.” Write the converse. Then decide whether it is true or false.

8. Let p be “an animal is a dog” and let q be “an animal is a golden retriever.” Write the inverse. Then decide whether it is true or false.

9. Let p be “an animal is a dog” and let q be “an animal is a golden retriever.” Write the contrapositive. Then decide whether it is true or false.

ID: A

3

If possible, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements.

10. If a figure is a square, then it is a rectangle. If a figure is a rectangle, then it has four right angles.

Decide whether inductive reasoning or deductive reasoning is used to reach the conclusion. Explain your reasoning.

11. All mammals are warm-blooded. Snakes are not warm-blooded. Your pet snake is not a mammal.

State the law of logic that is illustrated.

12. If you get an A on your math test, then you can choose where to go to dinner. If you can choose where to dinner, then you can go to your favorite restaurant.

If you get an A on your math test, then you can go to your favorite restaurant.

Determine which statements about the diagram you cannot conclude.

____ 13.

a. Line n and BD→←⎯⎯

intersect at point D. c. Points A, B, and C are collinear.b. Line m is perpendicular to plane S. d. Line m intersects plane S at point C.

Name the property that the statement illustrates.

14. If MN ≅ XY and XY ≅ RS, then MN ≅ RS

ID: A

4

15. CD ≅ CD

16. ∠EFG ≅ ∠EFG

Identify the numbered statement or reason in the two-column proof.

Given ∠ABC is a right angle.Prove x = 8

STATEMENTS REASONS1. ∠ABC is a right angle. 1. Given2. m∠ABC = 90° 2. 3. 3. Angle Addition Postulate4. (6x + 5)° + (5x − 3)° = 90° 4. Substitution Property of

Equality5. 11x + 2 = 90 5. Simplify.6. 6. Subtraction Property of

Equality7. x = 8 7.

____ 17. What is Reason 2?a. Given c. Definition of complementary anglesb. Definition of a right angle d. Angle Addition Postulate

ID: A

5

18. Find the values of x and y.

19. Each yard line of a football field is parallel to the yard line immediately to the right of it. Explain why the left 10-yard line is parallel to the right 10-yard line.

20. Find the value of x that makes a Ä b if c ll d.

ID: A

6

____ 21. Find the distance from point P to RQ.

a. 58 units c. about 7.6 unitsb. about 7.1 units d. 10 units

22. Determine which of the lines are parallel and which of the lines are perpendicular.

23. Write an equation of the line passing through the point (4, 6) that is parallel to the line y = 8x − 11.

ID: A

7

24. An architect is designing a garden for a client on a planning sheet. The client requests the relocation of a water fountain by the rule x, yÊ

ËÁÁˆ¯̃̃ → x + 9, y − 9Ê

ËÁÁˆ¯̃̃. Later, the client decides that they would prefer the

water fountain’s location moved from this new position 5 units left and 2 units down. Find the composition as a single transformation.

25. In the diagram, name the vector and select its component form.

____ 26. A student wants to apply a series of transformations to ABC. The student first applies a translation to the triangle, but then must decide whether to apply a reflection. Select all transformations used by the student to create the image AʺBʺC ʺ.

a. reflection in x-axis c. reflection in y-axisb. x, yÊ

ËÁÁˆ¯̃̃ → x − 4, y + 3Ê

ËÁÁˆ¯̃̃ d. x, yÊ

ËÁÁˆ¯̃̃ → x + 3, y + 4Ê

ËÁÁˆ¯̃̃

ID: A

8

27. Graph AB with endpoints A(3, –4) and B(3, 1) and its image after a reflection in the line y = x.

28. Graph the polygon and its image after a rotation of 270° counterclockwise about the origin.

29. In the diagram, the figure is reflected in line a. The image is then reflected in line b. Describe a single transformation that maps F to F ʺ.

30. Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement.

ID: A

9

31. Find m∠KMN.

____ 32. Classify PQR by its sides. Then determine whether it is a right triangle.

a. isoceles ; not right c. isoceles ; rightb. scalene ; right d. scalene ; not right

ID: A

10

33. Find the value of x.

34. Find the value of x.

ID: A

11

35. In the diagram of the roller coaster track below, can you use the Hypotenuse-Leg Congruence Theorem to prove that RSQ ≅ TQS?

Can the triangles be proven congruent with the information given in the diagram? If so, state the theorem you would use.

36.

ID: A

12

37. A road crew uses the triangles shown in the diagram to measure the width of a sink hole across a highway from a safe distance away. How wide is the sink hole?

38. In the diagram, AD→⎯⎯⎯

bisects ∠BAC. Find BD .

ID: A

13

39. Find AC.

40. A company builds trusses to support structures. In the truss shown below, the support GH is the midsegment of ABC. Find the value of x.

ID: A

14

41. You install fencing around your large triangular garden. Then, you divide it into four small triangular gardens by connecting the midpoints of each side of the triangle with fencing. How many feet of fencing do you need?

42. List the sides of ABC from shortest to longest.

____ 43. A triangle has one side that measures 3 feet and another side that measures 30 inches. Which are possible side lengths of the third side? a. 1 in. c. 72 in.b. 42 in. d. 30 in.

ID: A

15

44. For an art project you need to create a design that involves only triangles. One of the triangles you cut out is shown below. List the angles of ABC in order from smallest to largest.

45. Complete the statement AD___CD with <, >, or =.

ID: A

1

Geometry Semester 1 REVIEWAnswer Section

1. ANS: plane CAD, plane BFG

2. ANS: 23

3. ANS: 1,−8ÊËÁÁ

ˆ¯̃̃

4. ANS: 27 square units

5. ANS: 58°

6. ANS: 155°

7. ANS: If an animal is a golden retriever, then it is a dog; true

8. ANS: If an animal is not a dog, then it is not a golden retriever; true

9. ANS: If an animal is not a golden retriever, then it is not a dog; false

10. ANS: If a figure is a square, then it has four right angles.

11. ANS: deductive reasoning; Facts are used.

12. ANS: Law of Syllogism

13. ANS: B, C 14. ANS:

Transitive Property of Segment Congruence 15. ANS:

Reflexive Property of Segment Congruence 16. ANS:

Reflexive Property of Angle Congruence 17. ANS: B 18. ANS:

x = 3, y = 13 19. ANS:

By The Transitive Property of Parallel Lines, the left 10-yard line is parallel to the right 10-yard line. 20. ANS:

50 21. ANS: B 22. ANS:

a Ä bc⊥ a c⊥b

ID: A

2

23. ANS: y = 8x − 26

24. ANS: x, yÊËÁÁ

ˆ¯̃̃ → x + 4, y − 11Ê

ËÁÁˆ¯̃̃

25. ANS: CB→⎯⎯

, −2,−5

26. ANS: A, D 27. ANS:

28. ANS:

29. ANS: 40° rotation about point J

30. ANS: 94

; enlargement

31. ANS: 105°

32. ANS: C 33. ANS:

4

ID: A

3

34. ANS: 60

35. ANS: yes

36. ANS: yes; AAS Congruence Theorem

37. ANS: 18 ft

38. ANS: BD = 24

39. ANS: AC = 50

40. ANS: 10 ft

41. ANS: 216 ft

42. ANS: AB, AC, CB

43. ANS: B, D 44. ANS:

∠B, ∠C, ∠A 45. ANS:

=

ID: AGeometry Semester 1 REVIEW [Answer Strip]

_____13.B, C

_____17.B

_____21.B

_____26.A, D

_____32.C

_____43.B, D

Name: ______________________ Class: _________________ Date: _________ ID: B

1

Geometry Semester 1 REVIEW

Decide whether inductive reasoning or deductive reasoning is used to reach the conclusion. Explain your reasoning.

1. All mammals are warm-blooded. Snakes are not warm-blooded. Your pet snake is not a mammal.

____ 2. A triangle has one side that measures 3 feet and another side that measures 30 inches. Which are possible side lengths of the third side? a. 30 in. c. 72 in.b. 42 in. d. 1 in.

3. You install fencing around your large triangular garden. Then, you divide it into four small triangular gardens by connecting the midpoints of each side of the triangle with fencing. How many feet of fencing do you need?

4. Graph AB with endpoints A(3, –4) and B(3, 1) and its image after a reflection in the line y = x.

5. Graph the polygon and its image after a rotation of 270° counterclockwise about the origin.

ID: B

2

6. For an art project you need to create a design that involves only triangles. One of the triangles you cut out is shown below. List the angles of ABC in order from smallest to largest.

Name the property that the statement illustrates.

7. ∠EFG ≅ ∠EFG

8. If MN ≅ XY and XY ≅ RS, then MN ≅ RS

9. CD ≅ CD

10. Let p be “an animal is a dog” and let q be “an animal is a golden retriever.” Write the converse. Then decide whether it is true or false.

ID: B

3

11. Each yard line of a football field is parallel to the yard line immediately to the right of it. Explain why the left 10-yard line is parallel to the right 10-yard line.

12. The figure below is a rectangular shipping box. Name two different planes that contain BC→←⎯⎯

.

13. Find m∠BDC.

ID: B

4

14. In the diagram, AD→⎯⎯⎯

bisects ∠BAC. Find BD .

15. Determine which of the lines are parallel and which of the lines are perpendicular.

ID: B

5

16. A ramp that is used to load a truck makes supplementary angles with the ground. The ramp has an incline (∠1) of 25°. What is the measure of ∠2?

17. In the diagram, name the vector and select its component form.

ID: B

6

18. Find the value of x that makes a Ä b if c ll d.

19. Let p be “an animal is a dog” and let q be “an animal is a golden retriever.” Write the contrapositive. Then decide whether it is true or false.

20. Find the value of x.

21. The endpoints of GH are G −6,−9ÊËÁÁ

ˆ¯̃̃ and H 8,−7Ê

ËÁÁˆ¯̃̃. Find the coordinates of the midpoint M.

ID: B

7

____ 22. Classify PQR by its sides. Then determine whether it is a right triangle.

a. isoceles ; not right c. isoceles ; rightb. scalene ; not right d. scalene ; right

23. Complete the statement AD___CD with <, >, or =.

ID: B

8

24. Find the value of x.

25. Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement.

ID: B

9

26. A road crew uses the triangles shown in the diagram to measure the width of a sink hole across a highway from a safe distance away. How wide is the sink hole?

If possible, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements.

27. If a figure is a square, then it is a rectangle. If a figure is a rectangle, then it has four right angles.

28. Let p be “an animal is a dog” and let q be “an animal is a golden retriever.” Write the inverse. Then decide whether it is true or false.

ID: B

10

29. Find m∠KMN.

30. Find the values of x and y.

31. Find BC.

ID: B

11

Determine which statements about the diagram you cannot conclude.

____ 32.

a. Line m intersects plane S at point C. c. Line n and BD→←⎯⎯

intersect at point D.b. Line m is perpendicular to plane S. d. Points A, B, and C are collinear.

33. A company builds trusses to support structures. In the truss shown below, the support GH is the midsegment of ABC. Find the value of x.

34. List the sides of ABC from shortest to longest.

ID: B

12

____ 35. Find the distance from point P to RQ.

a. about 7.1 units c. 10 unitsb. 58 units d. about 7.6 units

36. Find AC.

State the law of logic that is illustrated.

37. If you get an A on your math test, then you can choose where to go to dinner. If you can choose where to dinner, then you can go to your favorite restaurant.

If you get an A on your math test, then you can go to your favorite restaurant.

ID: B

13

38. Write an equation of the line passing through the point (4, 6) that is parallel to the line y = 8x − 11.

39. Find the area of FGH with coordinates F −4,−6ÊËÁÁ

ˆ¯̃̃,G 1,3Ê

ËÁÁˆ¯̃̃, and H 2,−6Ê

ËÁÁˆ¯̃̃.

40. In the diagram, the figure is reflected in line a. The image is then reflected in line b. Describe a single transformation that maps F to F ʺ.

Can the triangles be proven congruent with the information given in the diagram? If so, state the theorem you would use.

41.

ID: B

14

42. An architect is designing a garden for a client on a planning sheet. The client requests the relocation of a water fountain by the rule x, yÊ

ËÁÁˆ¯̃̃ → x + 9, y − 9Ê

ËÁÁˆ¯̃̃. Later, the client decides that they would prefer the

water fountain’s location moved from this new position 5 units left and 2 units down. Find the composition as a single transformation.

43. In the diagram of the roller coaster track below, can you use the Hypotenuse-Leg Congruence Theorem to prove that RSQ ≅ TQS?

____ 44. A student wants to apply a series of transformations to ABC. The student first applies a translation to the triangle, but then must decide whether to apply a reflection. Select all transformations used by the student to create the image AʺBʺC ʺ.

a. reflection in x-axis c. x, yÊËÁÁ

ˆ¯̃̃ → x − 4, y + 3Ê

ËÁÁˆ¯̃̃

b. reflection in y-axis d. x, yÊËÁÁ

ˆ¯̃̃ → x + 3, y + 4Ê

ËÁÁˆ¯̃̃

ID: B

15

Identify the numbered statement or reason in the two-column proof.

Given ∠ABC is a right angle.Prove x = 8

STATEMENTS REASONS1. ∠ABC is a right angle. 1. Given2. m∠ABC = 90° 2. 3. 3. Angle Addition Postulate4. (6x + 5)° + (5x − 3)° = 90° 4. Substitution Property of

Equality5. 11x + 2 = 90 5. Simplify.6. 6. Subtraction Property of

Equality7. x = 8 7.

____ 45. What is Reason 2?a. Angle Addition Postulate c. Givenb. Definition of complementary angles d. Definition of a right angle

ID: B

1

Geometry Semester 1 REVIEWAnswer Section

1. ANS: deductive reasoning; Facts are used.

2. ANS: A, B 3. ANS:

216 ft 4. ANS:

5. ANS:

6. ANS: ∠B, ∠C, ∠A

7. ANS: Reflexive Property of Angle Congruence

8. ANS: Transitive Property of Segment Congruence

9. ANS: Reflexive Property of Segment Congruence

10. ANS: If an animal is a golden retriever, then it is a dog; true

ID: B

2

11. ANS: By The Transitive Property of Parallel Lines, the left 10-yard line is parallel to the right 10-yard line.

12. ANS: plane CAD, plane BFG

13. ANS: 58°

14. ANS: BD = 24

15. ANS: a Ä bc⊥ a c⊥b

16. ANS: 155°

17. ANS: CB→⎯⎯

, −2,−5

18. ANS: 50

19. ANS: If an animal is not a golden retriever, then it is not a dog; false

20. ANS: 60

21. ANS: 1,−8ÊËÁÁ

ˆ¯̃̃

22. ANS: C 23. ANS:

= 24. ANS:

4 25. ANS:

94

; enlargement

26. ANS: 18 ft

27. ANS: If a figure is a square, then it has four right angles.

28. ANS: If an animal is not a dog, then it is not a golden retriever; true

29. ANS: 105°

30. ANS: x = 3, y = 13

31. ANS: 23

32. ANS: B, D

ID: B

3

33. ANS: 10 ft

34. ANS: AB, AC, CB

35. ANS: A 36. ANS:

AC = 50 37. ANS:

Law of Syllogism 38. ANS:

y = 8x − 26 39. ANS:

27 square units 40. ANS:

40° rotation about point J 41. ANS:

yes; AAS Congruence Theorem 42. ANS:

x, yÊËÁÁ

ˆ¯̃̃ → x + 4, y − 11Ê

ËÁÁˆ¯̃̃

43. ANS: yes

44. ANS: A, D 45. ANS: D

ID: BGeometry Semester 1 REVIEW [Answer Strip]

_____ 2.A, B

_____22.C

_____32.B, D

_____35.A

_____44.A, D

_____45.D