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Ultimate Geometry Regents Knowledge Practice

Total questions: 125

Worksheet time: 10hrs 25mins

Name
Class
Date
1.

Which of the following is the correct midpoint formula given two endpoints (x1, y1) and (x2, y2)?

a)
b)
c)
d)
2.
On the coordinate plane, which line is the y-axis?
a)
Horizontal Line (Side to Side)
b)
Vertical Line (Up and Down)
3.

How is the distance formula correctly written:

a)

d = (y1 − y2)2 −(x2 − x1)2 d\ =\ \sqrt{\left(y_{1\ }-\ y_2\right)^2\ -\left(x_{2\ }-\ x_1\right)^2}\

b)

d = (x2 − x1)2 + (y2 − y1 )2d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2_{\ }}-\ y_1\ \right)2}

c)

d = (y1 − y 2)2 + (x2 − x1)2d\ =\ \sqrt{\left(y_{1\ }-\ y\ _2\right)^2\ +\ \left(x_{2\ }-\ x_1\right)}^2

d)

d = (x)2− (y)2\sqrt{\left(x\right)^2-\ \left(y\right)^2}

4.
The Pythagorean Theorem ONLY works on which triangle? 
a)
obtuse
b)
scalene
c)
isosceles
d)
right
5.

The Pythagorean Theorem is
a2 + b2 = c2

a)
false
b)
true
6.
What is the longest side of a right triangle called?
a)
A. Leg A
b)
B. Leg B
c)
C. Hypotenuse
d)
D. Pythagorean Theorem
7.

What is the slope formula?

a)
b)
c)
d)
8.

What is the point-slope formula?

a)

b)

c)

d)

9.
Slopes of parallel lines are...
a)
opposite reciprocals.
b)
opposites.
c)
the same.
d)
always 7.
10.
Slopes of perpendicular lines are...
a)
opposite reciprocals.
b)
opposites.
c)
identical.
d)
always 7.
11.
What slope is parallel to:  
m = 3/4
a)
4/3
b)
3/4
c)
-3/4
d)
-4/3
12.

What is the slope of a line perpendicular to 5?

a)

5

b)

1/5

c)

-1/5

d)

-5

13.
What term is used to describe a pair, or group, of angles that equal 180 degrees?
a)
Supplementary Angles
b)
Complementary Angles
c)
Vertical Angles
d)
Congruent Angles
14.
What is the formula for the volume of a prism?
a)
V = P*h
b)
V = B*h
c)
V = (1/3)P*h
d)
V = (1/3)B*h
15.
What is the formula for volume of a CONE?
a)
V = π r²
b)
V = π r² h
c)
V =  ⅓ π r² h
d)
V =  ⅓ L W H
16.
What is the formula for the volume of a pyramid?
a)
V = P*h
b)
V = B*h
c)
V = (1/3)P*h
d)
V = (1/3)B*h
17.
What is the volume formula for a sphere?
a)
V = (4 ∕ 3)πr3
b)
V = (1 ∕ 3)πr2h
c)
V = πr2h
d)
V = (1 ∕ 3)Bh
18.
What is the formula for volume of a CYLINDER?
a)
V = π r²
b)
V = π r² h
c)
V =  ⅓ π r² h
d)
V =  ⅓ L W H
19.
Does this picture show the diameter or radius of a circle?
a)
Diameter
b)
Radius
20.

How do these triangles appear to be similar?
(Hint: Look for non-labeled parts!)

a)

AA

b)

SAS

c)

SSS

d)

Not Similar

21.

What congruency postulate proves the triangles congruency?

a)

SAS

b)

ASA

c)

SSS

d)

HL

22.

Name the angle relationship.

a)

Same Side Interior

b)

Alternate Interior

c)

Corresponding

d)

Vertical Angles

23.

Name the angle relationship.

a)

Alternate Interior

b)

Alternate Exterior

c)

Corresponding

d)

Vertical Angles

24.

Which of these angles is NOT congruent to angle 5?

a)

Angle 6

b)

Angle 8

c)

Angle 1

d)

Angle 4

25.

What leg is considered the hypotenuse?

a)

Any side

b)

the side opposite the smallest angle

c)

the side opposite the right angle

d)

the side opposite the shortest leg

26.

Name the angle relationship.

a)

Alternate Interior

b)

Alternate Exterior

c)

Corresponding

d)

Vertical Angles

27.

Volume of a Rectangular Prism

a)
b)
c)
d)
28.

What is the formula for area of a circle given the radius?

a)

A = πr

b)

A = 2πr

c)

A = πd

d)

A = πr²

29.

What is the formula for the area of a triangle?

a)

bh

b)

lw

c)

s2

d)

1/2(bh)

30.

What is the formula for the area of a parallelogram?

a)

bh

b)

lw

c)

s2

d)

1/2(bh)

31.

How do you find the diameter of a circle

a)

Multiply by pi

b)

Multiply the radius by 2

c)

Divide the radius by 2

d)

It's impossible...

32.

What is the formula for the area of a rectangle?

a)

lw

b)

1/2*h(b1+b2)

c)

3.14(r)

d)

s2

33.

What is the formula for the volume of a sphere?

a)

V = πr2h

b)

V = 4πr2

c)

V = (4/3)πr2

d)

V = (4/3)πr3

34.

What is the volume formula for a cylinder?

a)

V = (4 ∕ 3)πr3

b)

V = (1 ∕ 3)πr2h

c)

V = πr2h

d)

V = (1 ∕ 3)Bh

35.

The longest side of a triangle would be located where on a triangle?

a)

Across from the smallest angle

b)

Across from the largest angle

c)

Cannot tell.

d)

Adjacent to the smallest side.

36.

Do the following side lengths form a triangle?
3, 10, 7

a)

Yes

b)

No

37.

Name the angle relationship.

a)

Alternate Exteriors

b)

Alternate Interiors

c)

Corresponding

d)

Same Side Interiors

38.

Name the angle relationship.

a)

Alternate Interior

b)

Alternate Exterior

c)

Corresponding

d)

Vertical Angles

39.

What can you find with trig ratios?

a)

Missing sides

b)

missing angles

c)

area of a triangle

d)

missing sides, angles and area of a triangle

40.

Identify the transformation from B to D.

a)

90o Clockwise Rotation

b)

180o Rotation

c)

270o clockwise Rotation

d)

360o Rotation

41.

State the line of reflection.

a)

Reflection across y-axis

b)

Reflection across x-axis

c)

Reflection across x = 1

d)

Reflection across y = 1

42.

How is triangle ABC being translated to triangle A'B'C'?

a)

up 3, left 8

b)

up 9, left 4

c)

down 3, right 8

d)

down 9, right 4

43.

Find the largest side in Δ BCD

a)

Segment BC

b)

Segment DB

c)

Segment DC

d)

Segment AB

44.

Describe the possible lengths for the third side of the triangle given the two sides 10 and 5.

a)

5 < x 10

b)

0 < x < 10

c)

0 < x < 15

d)

5 < x < 15

45.

What postulate proves these triangles congruent?

a)

SAS

b)

ASA

c)

AAS

d)

Not enough information

46.

What postulate would prove triangle ∆NYQ is congruent to ∆PYQ?

a)

ASA

b)

SAS

c)

SSS

d)

HL

47.
Slopes of parallel lines are...
a)
opposite reciprocals.
b)
opposites.
c)
identical.
d)
always 7.
48.
Slopes of perpendicular lines are...
a)
opposite reciprocals.
b)
opposites.
c)
identical.
d)
always 7.
49.
A line is perpendicular to    y = 2x - 7.
What is the slope of this line? 
a)
-2
b)
1/2
c)
-1/2
d)
2
50.
What is the acronym to help you remember the ratios to use in trigonometry?
a)
RIGHTANG
b)
SOHCAHTOA
c)
SHOCHATOA
51.
What leg is considered the hypotenuse?
a)
Any side
b)
the side opposite the smallest angle
c)
the side opposite the right angle
d)
the side opposite the shortest leg
52.
What does "m" represent in y=mx+b?
a)
y-intercept
b)
slope
c)
macaroni
d)
nothing
53.
What is the relationship of the angles?
a)
Corresponding angles
b)
Same Side Interior
c)
Alternate Interior
d)
Alternate Exterior
54.
Which pair of angles are alternate exterior angles?
a)
Angle 7 and Angle 4
b)
Angle 2 and Angle 6
c)
Angle 8 and Angle 1
d)
Angle 2 and Angle 8
55.
Find missing side
a)
5
b)
7
c)
9
d)
11
56.
Find side length X.
a)
22.5
b)
10
c)
9
d)
7.5
57.
What does CPCTC stand for?
a)
Congruent parts of congruent triangles are congruent
b)
Corresponding parts of congruent triangles are congruent
c)
Corresponding parts of corresponding triangles are corresponding
d)
Corresponding parts of congruent triangles are Canadian.
58.
What does SAS stand for?
a)
Side-Angle-Side
b)
Super-Awesome-Side
c)
Side-Angle-Supersized
d)
Sensationally Awesome Superman
59.
What is m<1?
a)
25º
b)
75º
c)
115º
d)
65º
60.
What shortcut does NOT show congruent triangles?
a)
SSS
b)
AAS
c)
SSA
d)
ASA
61.
What shortcut does NOT show congruent triangles?
a)
SSS
b)
AAA
c)
AAS
d)
SAA
62.
What is the value of x?
a)
12
b)
11
c)
8
d)
6
63.
What is the volume formula for a cylinder?
a)
V = (4 ∕ 3)πr3
b)
V = (1 ∕ 3)πr2h
c)
V = πr2h
d)
V = (1 ∕ 3)Bh
64.
Area of a square:
a)
A=½bh
b)
A=πr2
c)
A=s2
d)
A=s+s+s+s
65.
The following formula is for the volume of:
V=πr2h
a)
Cylinder
b)
Cone
c)
Triangular Prism
d)
Sphere
66.
a)
b)
c)
d)
67.

area of trapazoid

a)

1/2(b1 + b2)

b)

h(b1 + b2)

c)

1/2h(b1 + b2)

d)

(b1 + b2)

68.
a)
Volume of a Pyramid
b)
Volume of a Sphere
c)
Volume of a Cylinder
69.

What is the Slope Intercept Formula

a)

ax + by = c

b)

y = mx + b

c)
d)
70.

What is the formula for the standard form of an equation?

a)

ax + by = c

b)

y = mx + b

c)
d)
71.

What equation would I pick for vertical angles?

a)

x = x

b)

x + x = 90

c)

x + x = 180

d)

x + x = 360

e)

x + x + x = 180

72.

What equation would I pick for complementary angles?

a)

x = x

b)

x + x = 90

c)

x + x = 180

d)

x + x = 360

e)

x + x + x = 180

73.

What equation would I pick for supplementary angles?

a)

x = x

b)

x + x = 90

c)

x + x = 180

d)

x + x = 360

e)

x + x + x = 180

74.

What equation would I pick for angles at a point?

a)

x = x

b)

x + x = 90

c)

x + x = 180

d)

x + x = 360

e)

x + x + x = 180

75.

What equation would I pick for angles of a triangle?

a)

x = x

b)

x + x = 90

c)

x + x = 180

d)

x + x = 360

e)

x + x + x = 180

76.

What shape has 3 sides?

a)

Triangle

b)

Quadrilateral

c)

Hexagon

d)

Decagon

77.

What shape has 4 sides?

a)

Triangle

b)

Quadrilateral

c)

Hexagon

d)

Decagon

78.

What shape has 5 sides?

a)

Octagon

b)

Pentagon

c)

Hexagon

d)

Decagon

79.

What shape has 6 sides?

a)

Octagon

b)

Pentagon

c)

Hexagon

d)

Decagon

80.

What shape has 7 sides?

a)

Octagon

b)

Septagon/Heptagon

c)

Nonagon

d)

Decagon

81.

What shape has 8 sides?

a)

Octagon

b)

Septagon/Heptagon

c)

Nonagon

d)

Decagon

82.

What shape has 9 sides?

a)

Octagon

b)

Septagon/Heptagon

c)

Nonagon

d)

Decagon

83.

What shape has 10 sides?

a)

Octagon

b)

Dodecagon

c)

Nonagon

d)

Decagon

84.

What shape has 12 sides?

a)

Octagon

b)

Dodecagon

c)

Nonagon

d)

Decagon

85.

What triangle has no sides congruent?

a)

Scalene

b)

Isosceles

c)

Equilateral

86.

What triangle has no angles congruent?

a)

Scalene

b)

Isosceles

c)

Equilateral

87.

What triangle has two angles congruent?

a)

Scalene

b)

Isosceles

c)

Equilateral

88.

What triangle has two sides congruent?

a)

Scalene

b)

Isosceles

c)

Equilateral

89.

What triangle has three sides congruent?

a)

Scalene

b)

Isosceles

c)

Equilateral

90.

What triangle has three angles congruent?

a)

Scalene

b)

Isosceles

c)

Equilateral

91.

Which is the correct formula for the area of a triangle using trig?

a)

A = 1/2 ab sinC

b)

A = 1/2 bc sinA

c)

A = 1/2 ac sinB

92.

What is NOT an acceptable response for saying two triangles are congruent?

a)

The transformations performed are rigid motions.

b)

The triangles are congruent because of SSS

c)

The transformation performed are dilations.

93.

What is equal to cosA?

a)

sinB

b)

tanA

c)

cosB

d)

sinA

94.

sin A = cos B. What do I know about A & B?

a)

A = B

b)

A + B = 180

c)

A + B = 90

d)

A + B = 360

95.

What point of concurrency is listed shown in the picture?

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

96.

What point of concurrency is listed shown in the picture?

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

97.

What point of concurrency is listed shown in the picture?

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

98.

What point of concurrency is listed shown in the picture?

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

99.

The point of concurrency created by perpendicular bisectors is called

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

100.

The point of concurrency created by angle bisectors is called

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

101.

The point of concurrency created by medians is called

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

102.

The point of concurrency created by altitudes is called

a)

Circumcenter

b)

Incenter

c)

Centroid

d)

Orthocenter

103.

The volume of a triangular prism is

a)

V = 1/2 b h h

b)

V = b h h

c)

V = 1/2 b h

104.

When dilating a line, if the center of dilation is ON the line, then the equation is

a)

The same

b)

The same slope different y-intercept

c)

Different slope same y-intercept

d)

Different slop different y-intercept

105.

When dilating a line, if the center of dilation is NOT on the line, then the equation is

a)

The same

b)

The same slope different y-intercept

c)

Different slope same y-intercept

d)

Different slop different y-intercept

106.

What is the correct trig equation?

a)

sin A = 8/13

b)

sin A = 13/8

c)

cos A = 8/13

d)

tan A = 13/8

107.

What is the correct trig equation to solve?

a)

cos θ = 47/100

b)

cos θ = 100/47

c)

sin θ = 47/100

d)

sin θ = 100/47

108.

What trig equation should you use to solve?

a)

tan θ = 45/27

b)

tan θ = 27/45

c)

sin θ = 45/27

d)

sin θ = 27/45

109.

Is this a HLLS or SAAS problem?

a)

HLLS

b)

SAAS

110.

Is this a HLLS or SAAS problem?

a)

HLLS

b)

SAAS

111.

What type of angle is shown in the picture?

a)

Central

b)

Inscribed

112.

What type of angle is shown in the picture?

a)

Central

b)

Inscribed

113.

What type of angle is shown in the picture?

a)

Central

b)

Inscribed

114.

What do we know about the angle compared to the intercepted arc?

a)

angle and arc are equal

b)

angle is half the arc

115.

What do we know about the angle compared to the intercepted arc?

a)

angle and arc are equal

b)

angle is half the arc

116.

What do we know about the angle compared to the intercepted arc?

a)

angle and arc are equal

b)

angle is half the arc

117.
inscribed angle: an angle with its vertex _____________ the circle
a)
at the center of
b)
on
118.
A ____ angle is an angle whose vertex is a the center of a circle.
a)
supplementary
b)
complimentary
c)
central
d)
obtuse
e)

inscribed

119.

Which formula would you use?

a)

2*angle = arc

b)

2*angle = arc + arc

c)

2*angle = arc - arc

d)

outside*whole = outside*whole

e)

piece*piece = piece*piece

120.

Which formula would you use?

a)

2*angle = arc

b)

2*angle = arc + arc

c)

2*angle = arc - arc

d)

outside*whole = outside*whole

e)

piece*piece = piece*piece

121.

Which formula would you use?

a)

2*angle = arc

b)

2*angle = arc + arc

c)

2*angle = arc - arc

d)

outside*whole = outside*whole

e)

piece*piece = piece*piece

122.

Which formula would you use?

a)

2*angle = arc

b)

2*angle = arc + arc

c)

2*angle = arc - arc

d)

outside*whole = outside*whole

e)

piece*piece = piece*piece

123.

Which formula would you use?

a)

2*angle = arc

b)

2*angle = arc + arc

c)

2*angle = arc - arc

d)

outside*whole = outside*whole

e)

piece*piece = piece*piece

124.

Which formula would you use?

a)

2*angle = arc

b)

2*angle = arc + arc

c)

2*angle = arc - arc

d)

outside*whole = outside*whole

e)

piece*piece = piece*piece

125.

Which formula would you use?

a)

2*angle = arc

b)

2*angle = arc + arc

c)

2*angle = arc - arc

d)

outside*whole = outside*whole

e)

piece*piece = piece*piece

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