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Geometry Finals

Total questions: 29

Worksheet time: 2hrs 18mins

Name
Class
Date
1.

If you move the point to change the original triangle, what happens to the sum of the interior angles?

a)

It remains the same

b)

It becomes zero

c)

It increases

d)

It decreases

2.

Do you think it is possible to have a triangle with angles 50°, 60°, and 80°? Explain.

a)

No, because the sum is not 180°

b)

No, because the angles are too small

c)

Yes, because the angles add up to 180°

d)

Yes, because any three angles can form a triangle

3-8.

Answer the questions below after watching the video

3.

What is the sum of the interior angles of a triangle?

a)

90 degrees

b)

270 degrees

c)

180 degrees

d)

360 degrees

4.

If one angle in a scalene triangle is 50 degrees, what is true about the other angles?

a)

They are both 50 degrees

b)

They are equal to each other

c)

They are both less than 130 degrees

d)

One is greater than 50 degrees and the other is less

5.

What does the exterior angle theorem state?

a)

The exterior angle is equal to the sum of the two adjacent interior angles

b)

The exterior angle is equal to the sum of the two opposite interior angles

c)

The sum of the exterior angles is 360 degrees

d)

The exterior angle is twice the sum of the interior angles

6.

If a triangle has angles measuring 51 and 47 degrees, what is the measure of the third angle?

a)

92 degrees

b)

78 degrees

c)

88 degrees

d)

82 degrees

7.

What is the measure of an angle that forms a linear pair with an 82-degree angle?

a)

180 degrees

b)

98 degrees

c)

90 degrees

d)

82 degrees

8.

In an isosceles triangle, if one base angle is 44 degrees, what is the measure of the other base angle?

a)

136 degrees

b)

90 degrees

c)

44 degrees

d)

88 degrees

9-13.

Answer the questions below after watching the video

9.

What is the term used to describe a four-sided polygon?

a)

Quadrilateral

b)

Triangle

c)

Hexagon

d)

Pentagon

10.

What is the sum of the interior angles of a triangle?

a)

180 degrees

b)

360 degrees

c)

270 degrees

d)

90 degrees

11.

How many triangles can be formed inside a hexagon?

a)

5

b)

4

c)

6

d)

3

12.

What is the sum of the interior angles of a pentagon?

a)

540 degrees

b)

360 degrees

c)

720 degrees

d)

180 degrees

13.

What is the measure of each interior angle in a regular pentagon?

a)

150 degrees

b)

135 degrees

c)

120 degrees

d)

108 degrees

14-20.

Answer the questions below after watching the video

14.

What is the formula for the sum of interior angles in a polygon?

a)

n - 2 * 180

b)

n * 180

c)

(n - 2) * 180

d)

180n - 360

15.

What formula is used when you know the measurement of one angle in a polygon?

a)

n - 2 * 180

b)

180n - 360

c)

n * 180

d)

(n - 2) * 180 / n

16.

What does 'n' represent in the polygon formulas?

a)

Number of angles

b)

Number of sides

c)

Sum of interior angles

d)

Measure of one interior angle

17.

How do you remove the denominator when solving for 'n' in the equation?

a)

Add n

b)

Subtract n

c)

Multiply by n

d)

Divide by n

18.

After isolating 'n', what is the next step to find its value?

a)

Apply the distributive property

b)

Subtract 'n' from both sides

c)

Add 360 to both sides

d)

Divide by the coefficient of 'n'

19.

What mathematical operation is initially used to eliminate the denominator in the equation?

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

20.

What type of polygon is formed when each interior angle measures 108°?

a)

Triangle

b)

Quadrilateral

c)

Hexagon

d)

Pentagon

21-29.

Answer the questions below after watching the video

21.

What is the defining characteristic of parallel lines?

a)

They eventually meet at some point.

b)

They intersect at a 90-degree angle.

c)

They form a triangle.

d)

They never intersect and are always equidistant.

22.

If angle 1 measures 110 degrees, what is the measure of angle 3?

a)

90 degrees

b)

180 degrees

c)

110 degrees

d)

70 degrees

23.

Which statement is true about corresponding angles?

a)

They have equal measurements.

b)

They are always supplementary.

c)

They are on the interior side of the parallel lines.

d)

They are on opposite sides of the transversal.

24.

What is the measure of angle 5 if angle 1 is 110 degrees?

a)

70 degrees

b)

180 degrees

c)

110 degrees

d)

90 degrees

25.

Which angles are congruent to angle 1?

a)

Angles 6 and 8

b)

Angles 2 and 6

c)

Angles 2 and 4

d)

Angles 3, 5, and 7

26.

What type of angles are angles 3 and 5?

a)

Corresponding angles

b)

Alternate exterior angles

c)

Alternate interior angles

d)

Supplementary angles

27.

How are angles 1 and 7 classified?

a)

Corresponding angles

b)

Vertical angles

c)

Adjacent angles

d)

Alternate exterior angles

28.

What relationship do alternate exterior angles have?

a)

They are supplementary.

b)

They are congruent.

c)

They sum up to 90 degrees.

d)

They are adjacent angles.

29.

Which angles form a linear pair with an odd angle?

a)

Alternate interior angles

b)

Corresponding angles

c)

Even angles

d)

Vertical angles

30-34.

Answer the questions below after watching the video

30.

How can a square help us remember the sum of angles in a triangle?

a)

Multiply the square's angle sum by 2

b)

Divide the square's angle sum by 2

c)

Divide the square's angle sum by 4

d)

Add 180 to the square's angle sum

31.

What is the sum of the angles in a square?

a)

180 degrees

b)

360 degrees

c)

90 degrees

d)

270 degrees

32.

If a triangle has one angle measuring 90 degrees, what type of triangle could it be?

a)

Right

b)

Scalene

c)

Isosceles

d)

Equilateral

33.

What property of isosceles triangles helps determine the measure of its angles?

a)

One angle is always larger than the others

b)

Two angles are equal

c)

All angles are equal

d)

Two angles are always 90 degrees

34.

What characteristic defines an equilateral triangle?

a)

None of the sides are equal

b)

All sides are of different lengths

c)

Two sides are of equal length

d)

All sides are of equal length

35-37.

Answer the questions below after watching the video

35.

What is the term for a line that intersects two parallel lines?

a)

Perpendicular

b)

Segment

c)

Bisector

d)

Transversal

36.

Which angles are always equal when formed by a transversal?

a)

Exterior angles

b)

Adjacent angles

c)

Supplementary angles

d)

Corresponding angles

37.

What type of angles are equal when they are vertically opposite?

a)

Corresponding angles

b)

Vertically opposite angles

c)

Alternate interior angles

d)

Co-interior angles

38.
Find the slope of the line.
a)
Undefined
b)
0
c)
1
d)
-1
39.
Find the slope of the line that passes through 
(-4, 7) and (-6, -4)
a)
2/11
b)
-2/11
c)
11/2
d)
-11/2
40.
Write equation of the line containing (-3,4) and (-1,-2)
a)
y = -3x - 5
b)
y = -3x + 1
c)
y = -3x + 13
d)
y = 3x + 1
41.
Slopes of perpendicular lines are...
a)
negative reciprocals
b)
opposites
c)
identical
d)
flipped
42.
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
43.
These lines are....
y=2
x=11
a)
Parallel
b)
Perpendicular
c)
Neither
44.
y = 6x + 2
y = -6x + 2
These lines are...
a)
Parallel
b)
Perpendicular
c)
Neither
45.
Given you have two points and are asked to find the perpendicular bisector, what step should you do first?
a)
Skip the problem
b)
Find the distance between the two points
c)
Find the equation of the line
d)
Find the midpoint of the two given points
46.
Write the equation of the perpendicular bisector of the line AB given:
A(1,3) & B(-3,5)
a)
y = 2x + 4
b)
y = 2x + 6
c)
y = -2x + 6
d)
y = 2x - 6
47.
Write the equation of the perpendicular bisector of the line AB given:
A(3,1) & B(-3,6)
a)
y = -5/6x + 7/2
b)
y = 6/5x + 9/2
c)
y = 6/5x + 7/2
d)
y = 6/5x + 4
48.
Write the equation of the perpendicular bisector of the line AB given:
A(4,-2) & B(4,4)
a)
y = 2
b)
x = 1
c)
y = x + 1
d)
y = 1
49.
Write the equation of the perpendicular bisector of the line AB given:
A(-4,3) & B(4,3)
a)
y = 3
b)
x = 0
c)
y = x
d)
y = 0

50-57.

Answer the questions below after watching the video

50.

What analogy is used to introduce the concept of slope?

a)

Riding a rollercoaster

b)

Driving on a highway

c)

Climbing a mountain

d)

Flying a kite

51.

What does a positive slope indicate about the direction of a line?

a)

It remains constant

b)

It moves upwards from left to right

c)

It moves downwards from left to right

d)

It is vertical

52.

How is slope expressed in mathematical terms?

a)

Distance over time

b)

Rise over run

c)

Speed over distance

d)

Height over width

53.

What does the 'rise' in 'rise over run' represent?

a)

Horizontal movement

b)

Vertical movement

c)

Diagonal movement

d)

Circular movement

54.

What is the most reduced form of the slope 6 over 9?

a)

6 over 9

b)

2 over 3

c)

1 over 3

d)

3 over 6

55.

What is the slope of a line that rises 6 units and runs 3 units to the right?

a)

3 over 6

b)

2

c)

6 over 3

d)

1 over 2

56.

What does a negative slope indicate about the direction of a line?

a)

It moves downwards from left to right

b)

It moves upwards from left to right

c)

It remains constant

d)

It is vertical

57.

How is the slope of a line determined between two points on a graph?

a)

By drawing a circle through the points

b)

By finding the rise over run

c)

By measuring the angle of inclination

d)

By calculating the distance between the points

58-67.

Answer the questions below after watching the video

58.

What is the Distance Formula an extension of?

a)

The Pythagorean Theorem

b)

The Area of a Triangle

c)

The Quadratic Formula

d)

The Circle Equation

59.

How do you calculate the distance between two points on a graph?

a)

By measuring with a ruler

b)

By using the Distance Formula

c)

By estimating visually

d)

By counting the units between them

60.

What does subtracting the x-coordinates of two points give you?

a)

The hypotenuse length

b)

The slope of the line

c)

The vertical distance

d)

The horizontal distance

61.

What is the first step in applying the Distance Formula directly?

a)

Add the coordinates together

b)

Take the square root of the sum of squares

c)

Square the differences of x-coordinates

d)

Subtract the y-coordinates

62.

What does squaring the differences in the Distance Formula accomplish?

a)

It eliminates negative values

b)

It calculates the area of the triangle

c)

It finds the midpoint between two points

d)

It doubles the distance for accuracy

63.

What is the result of applying the Distance Formula to the points (-2, 4) and (2, -1)?

a)

Square root of 41

b)

Square root of 61

c)

6 units

d)

5 units

64.

Why do we square the differences when using the Distance Formula?

a)

To find the actual distance

b)

To comply with the Pythagorean Theorem

c)

To avoid negative distances

d)

To simplify the calculation

65.

What does the Distance Formula calculate?

a)

The distance between any two points

b)

The perimeter of a triangle

c)

The area under a curve

d)

The slope of a line

66.

How is the Distance Formula verified?

a)

By using a protractor

b)

By comparing with graph method results

c)

By measuring with a ruler on the graph

d)

By consulting a math textbook

67.

Why might one prefer the Distance Formula over graphing?

a)

It requires less time

b)

It is more accurate

c)

It does not require a graph

d)

It is easier to remember

68-77.

Answer the questions below after watching the video

68.

What is the general equation of a circle with center (h, k) and radius R?

a)

(x - h)^2 + (y - k)^2 = R

b)

x^2 + y^2 = R^2

c)

x^2 + y^2 = R

d)

(x - h)^2 + (y - k)^2 = R^2

69.

How do you find the distance between two points (x1, y1) and (x2, y2)?

a)

sqrt((x2 - x1)^2 + (y2 - y1)^2)

b)

sqrt((x2 + x1)^2 + (y2 + y1)^2)

c)

|x2 - x1| + |y2 - y1|

d)

(x2 - x1)^2 + (y2 - y1)^2

70.

What is the slope of a line perpendicular to another line with slope m?

a)

1/m

b)

-1/m

c)

-m

d)

-1/m^2

71.

How do you find the midpoint between two points (x1, y1) and (x2, y2)?

a)

(x1 + x2, y1 + y2)

b)

(x1 * x2, y1 * y2)

c)

((x1 + x2) / 2, (y1 + y2) / 2)

d)

((x1 - x2) / 2, (y1 - y2) / 2)

72.

What property do the perpendicular bisectors of chords in a circle have?

a)

They intersect at the circle's center

b)

They are parallel to the circle's radius

c)

They bisect the circle's area

d)

They form a right angle with the circle's diameter

73.

How is the equation of the perpendicular bisector of a segment derived?

a)

Using the midpoint and the slope of the segment

b)

Using the endpoints of the segment only

c)

Using the slope of the segment and one endpoint

d)

Using the midpoint and the perpendicular slope

74.

What method is used to solve the system of equations derived from the perpendicular bisectors?

a)

Graphical method

b)

Substitution

c)

Matrix method

d)

Addition or subtraction

75.

How do you determine the radius of the circle?

a)

By measuring the circumference of the circle

b)

By doubling the distance between the center and one of the points

c)

By finding the distance from the center to any point on the circle

d)

By calculating the area of the circle

76.

What is the center of the circle found in the example?

a)

(-8, -1)

b)

(8, 1)

c)

(1, 8)

d)

(8, -1)

77.

What is the final form of the equation of a circle found in the example?

a)

(x - 8)^2 + (y - 1)^2 = sqrt(29)

b)

(x + 8)^2 + (y + 1)^2 = 29

c)

x^2 + y^2 = 29

d)

(x - 8)^2 + (y - 1)^2 = 29

78-85.

Answer the questions below after watching the video

78.

What are the two parallel sides of a trapezoid called?

a)

Diagonals

b)

Legs

c)

Altitudes

d)

Bases

79.

How is the height of a trapezoid defined?

a)

Perpendicular distance from a vertex to the base

b)

Distance between the bases

c)

Length of the base

d)

Distance between any two points

80.

What is the first step in calculating the area of a trapezoid?

a)

Measure the diagonals

b)

Multiply the bases

c)

Divide into two triangles

d)

Add the bases

81.

What formula is used to calculate the area of each triangle in a trapezoid?

a)

Base times half height

b)

Half base times height

c)

Base plus height

d)

Base times height

82.

If one base of the trapezoid is 6 units and the height is also 6 units, what is the area of the triangle formed?

a)

18 square units

b)

12 square units

c)

36 square units

d)

24 square units

83.

What is the area of a triangle with a base of 7 units and height of 6 units?

a)

28 square units

b)

12 square units

c)

42 square units

d)

21 square units

84.

How do you find the total area of a trapezoid?

a)

Add the areas of the triangles

b)

Subtract the areas of the triangles

c)

Add the areas of the bases

d)

Multiply the areas of the triangles

85.

What is the total area of a trapezoid with triangle areas of 18 and 21 square units?

a)

39 square units

b)

40 square units

c)

34 square units

d)

36 square units

86.
Solve for x.
a)
16
b)
11
c)
50
d)
6
87.
What is the measure of angle b
a)
146
b)
34
c)
36
d)
136
88.

A student is trying to construct triangles using four different sets of angles. The angles in each set are given below. Which set will form a triangle?

a)

45°, 65°, 70°

b)

150°, 110°, 100°

c)

50°, 50°, 50°

d)

90°, 90°, 90°

89.
Find the measure of the angle indicated. 
a)
139°
b)
66°
c)
138°
d)
116°
90.
Challenge:  Find the measure of the indicated angle. 
a)
145 degrees
b)
24 degrees
c)
20 degrees 
d)
21 degrees