Download Semester 1 Geometry final exam Review

Name: ______________________
Class: _________________
Date: _________
ID: A
Geometry Semester 1 REVIEW
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⎯
→
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 ÊÁË −6, −9 ˆ˜¯ and H ÊÁË 8, −7 ˆ˜¯ . Find the coordinates of the midpoint M.
4. Find the area of
FGH with coordinates F ÊÁË −4, −6 ˆ˜¯ ,G ÊÁË 1, 3 ˆ˜¯ , and H ÊÁË 2, −6 ˆ˜¯ .
1
ID: A
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.
2
ID: A
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.
b.
←⎯
⎯
→
Line n and BD intersect at point D.
Line m is perpendicular to plane S.
c. Points A, B, and C are collinear.
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
3
ID: A
15. CD ≅ CD
16. ∠EFG ≅ ∠EFG
Identify the numbered statement or reason in the two-column proof.
Given
Prove
∠ABC is a right angle.
x=8
STATEMENTS
1. ∠ABC is a right angle.
2. m∠ABC = 90°
3.
4. (6x + 5)° + (5x − 3)° = 90°
5. 11x + 2 = 90
6.
7. x = 8
____ 17. What is Reason 2?
a. Given
b. Definition of a right angle
REASONS
1. Given
2.
3. Angle Addition Postulate
4. Substitution Property of
Equality
5. Simplify.
6. Subtraction Property of
Equality
7.
c. Definition of complementary angles
d. Angle Addition Postulate
4
ID: A
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.
5
ID: A
____ 21. Find the distance from point P to RQ.
a.
b.
58 units
about 7.1 units
c. about 7.6 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.
6
ID: A
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 ÊÁË x, y ˆ˜¯ → ÊÁË x + 9, y − 9 ˆ˜¯ . 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 A ʺ B ʺ C ʺ .
a.
b.
reflection in x-axis
ÁÊË x, y ˜ˆ¯ → ÁÊË x − 4, y + 3 ˜ˆ¯
c. reflection in y-axis
d. ÁÊË x, y ˜ˆ¯ → ÊÁË x + 3, y + 4 ˜ˆ¯
7
ID: A
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.
8
ID: A
31. Find m∠KMN.
____ 32. Classify
a.
b.
PQR by its sides. Then determine whether it is a right triangle.
isoceles ; not right
scalene ; right
c. isoceles ; right
d. scalene ; not right
9
ID: A
33. Find the value of x.
34. Find the value of x.
10
ID: A
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.
11
ID: A
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?
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⎯
→
38. In the diagram, AD bisects ∠BAC. Find BD .
12
ID: A
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.
13
ID: A
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.
14
ID: A
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 =.
15
ID: A
Geometry Semester 1 REVIEW
Answer Section
1. ANS:
plane CAD, plane BFG
2. ANS:
23
3. ANS:
ÁÊË 1, −8 ˜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:
aÄb
c⊥a
c⊥b
1
ID: A
23. ANS:
y = 8x − 26
24. ANS:
ÊÁ x, y ˆ˜ → ÊÁ x + 4, y − 11 ˆ˜
Ë
¯
Ë
¯
25. ANS:
⎯⎯
→
CB , −2, −5
26. ANS: A, D
27. ANS:
28. ANS:
29. ANS:
40° rotation about point J
30. ANS:
9
; enlargement
4
31. ANS:
105°
32. ANS: C
33. ANS:
4
2
ID: A
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:
=
3
Geometry Semester 1 REVIEW [Answer Strip]
ID: A
B
_____21.
C
_____32.
A, D
_____26.
B, D
_____43.
B, C
_____13.
B
_____17.
Name: ______________________
Class: _________________
Date: _________
ID: B
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.
1
ID: B
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.
2
ID: B
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.
3
ID: B
⎯⎯
⎯
→
14. In the diagram, AD bisects ∠BAC. Find BD .
15. Determine which of the lines are parallel and which of the lines are perpendicular.
4
ID: B
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.
5
ID: B
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 ÊÁË −6, −9 ˆ˜¯ and H ÊÁË 8, −7 ˆ˜¯ . Find the coordinates of the midpoint M.
6
ID: B
____ 22. Classify
a.
b.
PQR by its sides. Then determine whether it is a right triangle.
isoceles ; not right
scalene ; not right
c. isoceles ; right
d. scalene ; right
23. Complete the statement AD___CD with <, >, or =.
7
ID: B
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.
8
ID: B
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.
9
ID: B
29. Find m∠KMN.
30. Find the values of x and y.
31. Find BC.
10
ID: B
Determine which statements about the diagram you cannot conclude.
____ 32.
a.
b.
Line m intersects plane S at point C.
Line m is perpendicular to plane S.
←⎯
⎯
→
c. Line n and BD intersect at point D.
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.
11
ID: B
____ 35. Find the distance from point P to RQ.
a.
b.
about 7.1 units
58 units
c. 10 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.
12
ID: B
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 ÊÁË −4, −6 ˆ˜¯ ,G ÊÁË 1, 3 ˆ˜¯ , and H ÊÁË 2, −6 ˆ˜¯ .
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.
13
ID: B
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 ÊÁË x, y ˆ˜¯ → ÊÁË x + 9, y − 9 ˆ˜¯ . 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 A ʺ B ʺ C ʺ .
a.
reflection in x-axis
c.
b.
reflection in y-axis
d.
14
ÊÁ x, y ˆ˜ → ÊÁ x − 4, y + 3 ˆ˜
Ë
¯
Ë
¯
ÁÊË x, y ˜ˆ¯ → ÁÊË x + 3, y + 4 ˜ˆ¯
ID: B
Identify the numbered statement or reason in the two-column proof.
Given
Prove
∠ABC is a right angle.
x=8
STATEMENTS
1. ∠ABC is a right angle.
2. m∠ABC = 90°
3.
4. (6x + 5)° + (5x − 3)° = 90°
5. 11x + 2 = 90
6.
7. x = 8
REASONS
1. Given
2.
3. Angle Addition Postulate
4. Substitution Property of
Equality
5. Simplify.
6. Subtraction Property of
Equality
7.
____ 45. What is Reason 2?
a. Angle Addition Postulate
b. Definition of complementary angles
c. Given
d. Definition of a right angle
15
ID: B
Geometry Semester 1 REVIEW
Answer 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
1
ID: B
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:
aÄb
c⊥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:
ÁÊË 1, −8 ˜ˆ¯
22. ANS: C
23. ANS:
=
24. ANS:
4
25. ANS:
9
; enlargement
4
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
2
ID: B
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:
ÁÊË x, y ˜ˆ¯ → ÁÊË x + 4, y − 11 ˜ˆ¯
43. ANS:
yes
44. ANS: A, D
45. ANS: D
3
Geometry Semester 1 REVIEW [Answer Strip]
C
_____22.
ID: B
A
_____35.
B, D
_____32.
A, B 2.
_____
A, D
_____44.
D
_____45.