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Name: ________________________ Class: ___________________ Date: __________
Geometry - Semester 1 test Review - Sections 1-42
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which set of three points is collinear?
a.
b.
F, G, H
E, F, H
c.
d.
E, F, G
J, F, H
Use the diagram from the following problems.
____
2. Which pair of angles, if congruent, proves lines a and b are parallel?
d. ∠5 and ∠2
a. ∠3 and ∠7
b. ∠8 and ∠7
e. None correct
c. ∠8 and ∠6
____
3. If lines a and b are parallel and m∠8 = 76° , then what is m∠1 ?
d. 104°
a. 14°
b. 166°
e. None correct
c. 76°
1
ID: A
Name: ________________________
ID: A
____
4. Which of the following is a counterexample to the following conjecture? If x 2 = 100 , then x = 10 .
c. x = 100
a. x = −10
b. x = 10
d. x = −100
____
5. Which choice is a counterexample to the conjecture? If x < 5, then x 2 < 25 .
d. 9
a. –3
b. 5
e. None correct
c. –8
____
6. If ? ? ? ? =? ? , which length could be used to prove
Theorem?
a. ???? = ??
d.
b. ???? = ??
e.
c. ???? = ??
??????∼
? ? ? ? ? ? using the SAS Similarity
???? = ??
None correct
____
7. What is the order of ∠? ?, ∠? ?, and ∠? ? from least to greatest measure?
d. ∠? ? ,∠? ? ,∠? ?
a. ∠? ? ,∠? ? ,∠? ?
b. ∠? ? ,∠? ? ,∠? ?
e. None correct
c. ∠? ? ,∠? ? ,∠? ?
____
8. Solve the equation 4x − 6 = 34. Fill in the missing justifications.
4x − 6 = 34
Given
[1]
+6 +6
4x
= 40
Simplify.
40
4x
[2]
=
4
4
x = 10
Simplify.
a.
b.
c.
d.
[1] Substitution Property of Equality;
[2] Division Property of Equality
[1] Addition Property of Equality;
[2] Division Property of Equality
[1] Division Property of Equality;
[2] Subtraction Property of Equality
[1] Addition Property of Equality;
[2] Reflexive Property of Equality
2
Name: ________________________
____
9. Which line is parallel to y = 2x − 7 ?
a. y = x − 7
b. 3y − 6x = 0
1
c. y = − x
2
ID: A
d.
e.
−4y = 2x
None correct
____ 10. What is the minimum number of noncollinear points needed to identify exactly one plane?
a. one
d. four
b. two
e. None Correct
c. three
____ 11. Point B lies on AC between A and C. AB = 3x − 8 and BC = 5x + 3 . Find AC.
a. 8x − 5
c. 8x + 11
b. 8x − 11
d. 8x + 5
____ 12. Find the perimeter of a square if one side measures 6 inches.
a. 12 inches
c. 36 inches
b. 24 inches
d. 10 inches
____ 13. Identify two lines in the diagram.
←

→ ←
→
a.
QU , SV
c.
b.
Q, R
d.
QU , RV

→ 

→
3
SQ , QU
Name: ________________________
ID: A
____ 14. Identify the line segments that are congruent in the diagram.
a.
b.
LN ≅ LP ; NR ≅ PS ; NP ≅ RS
LN ≅ PS ; NR ≅ LN ; LP ≅ RS
c.
d.
RS ≅ LP ; NR ≅ NP ; PS ≅ RS
LR ≅ LS ; NR ≅ NP ; PS ≅ RS
____ 15. G is between F and H . FH = 6x, FG = 4x + 14, and GH = 31. Find FH .
a.
b.
FH = 135
FH = 51
c.
d.
FH = 22.5
FH = 104
____ 16. Name three rays in the diagram.

→ 
→ 
→
a.
L, M , P
c.
LP , MN , PM
←

→ ←
→ ←

→
b.
LP , LN , NP
d.
LM , NP , MP


→
____ 17. BD bisects ∠ABC , m∠ABD = (6x − 5)°, and m∠DBC = (2x + 7)°. Find m∠ABD.
c. m∠ABD = 13°
a. m∠ABD = 3°
b. m∠ABD = 26°
d. m∠ABD = 23°
4
Name: ________________________
ID: A
____ 18. m∠IJK = 56° and m∠IJL = 29°. Find m∠LJK .
a.
b.
m∠LJK = 27°
m∠LJK = −27°
c.
d.
←
→
m∠LJK = 58°
m∠LJK = 85°
←
→
____ 19. Tell whether the lines MR and PQ appear parallel, perpendicular, or skew.
a.
skew
b.
perpendicular
c.
parallel
____ 20. Use the diagram to tell whether the angles ∠CSN and ∠NSR are complementary, supplementary, or neither.
a.
complementary
b.
neither
c.
5
supplementary
Name: ________________________
ID: A
____ 21. Use the Pythagorean Theorem to find the missing side length.
a.
b.
24 ft
576 ft
c.
d.
12 ft
34.99 ft
c.
d.
CD = –9.5
CD = –6.5
____ 22. Find the length of CD.
a.
b.
CD = 7.5
CD = 6.5
____ 23. Tell whether the figure is a polygon. If it is a polygon, classify it.
a.
b.
polygon, decagon
polygon, hexagon
c.
d.
6
polygon, dodecagon
not a polygon
Name: ________________________
ID: A
____ 24. Tell whether the slope of the line is positive or negative. Then, determine the slope.
3
2
a.
positive;
b.
negative; − 3
2
7
c.
negative; − 4
d.
negative; − 2
7
3
Name: ________________________
____ 25. Graph the line with the equation y = 5x − 3 .
a.
b.
ID: A
c.
d.
____ 26. Write the contrapositive of the statement, “If a state's capital is Denver, then the state is Colorado.”
a. If a state is Colorado, then its capital is not Denver.
b. If a state is Colorado, then its capital is Denver.
c. If a state is not Colorado, then its capital is not Denver.
d. If a state's capital is not Denver, then the state is not Colorado.
____ 27. One of the acute angles in a right triangle has a measure of 16.6°. What is the measure of the other acute
angle?
a. 16.6°
c. 90°
b. 73.4°
d. 163.4°
8
Name: ________________________
ID: A
____ 28. Find m∠K .
a.
b.
m∠K = 63°
m∠K = 55°
c.
d.
m∠K = 79°
m∠K = 39°
____ 29. Determine if the biconditional is true. If false, give a counterexample.
A figure is a square if and only if it is a rectangle.
a. The biconditional is true.
b. The biconditional is false. A rectangle does not necessarily have four congruent sides.
c. The biconditional is false. All squares are parallelograms with four 90° angles.
d. The biconditional is false. A rectangle does not necessarily have four 90° angles.
____ 30. If all angles of a polygon are congruent, how can the polygon be classified?
a. It is equiangular.
c. It is equilateral.
b. It is irregular.
d. It is concave.
____ 31. Determine the slope of the line containing points ( 6, 9) and (4, 3).
1
c. −3
a. −
3
1
b.
d. 3
3
____ 32. Find the area of a trapezoid with parallel sides measuring 5 feet and 10 feet and a height of 3 feet.
a. 7.5 ft 2
c. 75 ft 2
b. 150 ft 2
d. 22.5 ft 2
9
Name: ________________________
ID: A
____ 33. If 16 = 2x − 4, then 2x − 4 = 16. This is an example of which property of equality?
a. addition
c. symmetric
b. subtraction
d. multiplication
____ 34. Find the area of the parallelogram.
a.
b.
18.5 cm2
37 cm2
c.
d.
71.5 cm2
143 cm2
c.
d.
240 in.2
18 in.2
____ 35. Find the area of the trapezoid.
a.
b.
720 in.2
180 in.2
10
Name: ________________________
ID: A
____ 36. Given: ∆ABC ≅ ∆MNO
Identify all pairs of congruent corresponding parts.
a.
b.
c.
d.
∠A ≅
∠A ≅
∠A ≅
∠A ≅
∠M , ∠B ≅ ∠N , ∠C ≅ ∠O,
∠M , ∠B ≅ ∠O, ∠C ≅ ∠N ,
∠M , ∠B ≅ ∠N , ∠C ≅ ∠O,
∠O, ∠B ≅ ∠N , ∠C ≅ ∠M ,
AB ≅
AB ≅
AB ≅
AB ≅
MN , BC ≅ NO, AC ≅
MN , BC ≅ NO, AC ≅
MO, BC ≅ NO, AC ≅
NO, BC ≅ MN , AC ≅
MO
MO
MN
MO
____ 37. What additional information do you need to prove ∆ABC ≅ ∆ADC by the SAS Postulate?
a.
b.
AB ≅ AD
∠ACB ≅ ∠ACD
c.
d.
11
∠ABC ≅ ∠ADC
BC ≅ DC
Name: ________________________
ID: A
____ 38. In ∆ABC , BY = 16.5 and CO = 15 . AX BY ,and CZ are medians. Find BO .
a.
b.
BO = 11
BO = 16.5
c.
d.
BO = 5.5
BO = 15
____ 39. Tell whether the given side lengths form a right triangle.
5, 7, 10
a. Yes
b. No
____ 40. Determine if you can use the Leg-Angle Congruence Theorem to prove ∆CBA ≅ ∆CED. Explain.
a.
b.
c.
d.
AC ≅ DC . However, no angles are known to be congruent, so LA cannot be applied.
AC and DC are hypotenuses, not legs, so LA cannot be applied. You would need to use
HA to prove that ∆CBA ≅ ∆CED.
AC ≅ DC . ∠CAB ≅ ∠CDE because both are right angles. Therefore, ∆CBA ≅ ∆CED by
LA.
AC ≅ DC . ∠ACB ≅ ∠DCE because vertical angles are congruent. Therefore,
∆CBA ≅ ∆CED by LA.
12
Name: ________________________
ID: A
____ 41. Determine if you can use the HL Congruence Theorem to prove ∆ACD ≅ ∆DBA. If not, tell what else you
need to know.
a.
b.
c.
d.
Yes.
No. You do not know that ∠C and ∠B are right angles.
No. You do not know that AC ≅ BD .
No. You do not know that AB Ä CD.
____ 42. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it.
a.
b.
∆LMN ≅ ∆TUV , HL
∆LMN ≅ ∆VTU , LL
c.
d.
∆LMN ≅ ∆TUV , LL
∆LMN ≅ ∆VTU , HL
____ 43. Write an equation in slope-intercept form for the line parallel to y = 9x – 7 that passes through the point (–2,
–7).
1
65
c. y = − 9 x – 9
a. y = 9x + 11
b.
1
y = −9 x – 7
d.
13
y = 9x – 16
Name: ________________________
ID: A
____ 44. Three towns, Maybury, Junesville, and Cyanna, will create one sports center. Where should the center be
placed so that it is the same distance from all three towns?
a. Treat the towns as vertices of a triangle. The center must be placed at the triangle’s
circumcenter.
b. Treat the towns as vertices of a triangle. The center must be placed at the triangle’s
incenter.
c. Treat the towns as sides of a triangle. The center must be placed at the triangle’s
circumcenter.
d. Treat the towns as sides of a triangle. The center must be placed at the triangle’s
incenter.
____ 45. The diagram shows the approximate distances from Houston to Dallas and from Austin to Dallas. What is the
range of distances, d, from Austin to Houston?
a.
b.
40 < d < 440
−40 < d < 440
c.
d.
200 < d < 240
0 < d < 440
____ 46. m∠ADC > m∠BDC , AC = 3x + 32, and BC = 7x + 16 . Find the range of values for x.
a.
b.
0<x<4
16
−7 <x<4
c.
d.
14
x>4
7
−8 < x < 4
Name: ________________________
ID: A
____ 47. Find a line that is parallel to y = 6x − 4 and passes through point (4, 1).
c. y = 6x − 23
a. y = 6x + 23
b. y = 6x − 3
d. y = 6x + 3
____ 48. What is the length of ? ? ? ??
a. 7
b. 7.2
c. 7.3
d.
e.
7.1
None correct
____ 49. Given the following similar triangles, find the length of UV .
a.
b.
7
2
c.
d.
Short Answer
50. Find the distance from P(–1, 2) to the line x = –4.
15
6
24
ID: A
Geometry - Semester 1 test Review - Sections 1-42
Answer Section
MULTIPLE CHOICE
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2.
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39.
C
A
D
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D
A
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A
A
B
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C
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B
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ID: A
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49.
D
A
B
A
A
A
B
C
B
C
SHORT ANSWER
50. 3
2