Polygons And Quadrilaterals Test-period 8

1. How many sides does a nonagon have?

9

More than 10

0

7

A nonagon is a polygon with nine sides. Therefore, the correct answer is 9.

Explanation

A nonagon is a polygon with nine sides. Therefore, the correct answer is 9.

2. How many sides does a pentagon have?

5

6

7

8

A pentagon is a polygon with five sides. Therefore, the correct answer is 5.

Explanation

A pentagon is a polygon with five sides. Therefore, the correct answer is 5.

3. Find the area:

120

60

23

30

not-available-via-ai

Explanation

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4. In a rhombus, the diagonals bisect the angles

True

False

In a rhombus, the diagonals bisect the angles. This means that each diagonal divides the angle formed by the adjacent sides into two equal parts. This property is true for all rhombuses, making the statement "True" the correct answer.

Explanation

In a rhombus, the diagonals bisect the angles. This means that each diagonal divides the angle formed by the adjacent sides into two equal parts. This property is true for all rhombuses, making the statement "True" the correct answer.

5. What's the measure of angle E?

115°

25°

65°

90°

The measure of angle E is 65° because it is the only option that is not a right angle (90°) and is not provided as a measurement in the question.

Explanation

The measure of angle E is 65° because it is the only option that is not a right angle (90°) and is not provided as a measurement in the question.

6. All squares are parallelograms

True

False

All squares are parallelograms because a square is a special type of parallelogram. A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. A square is a specific type of parallelogram where all four sides are equal in length and all angles are right angles. Therefore, since a square meets the criteria of a parallelogram, the statement "All squares are parallelograms" is true.

Explanation

All squares are parallelograms because a square is a special type of parallelogram. A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. A square is a specific type of parallelogram where all four sides are equal in length and all angles are right angles. Therefore, since a square meets the criteria of a parallelogram, the statement "All squares are parallelograms" is true.

7. In the rhombus below, what is x?

7.25

32

4

97.25

not-available-via-ai

Explanation

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8. In the trapezoid below, what is x if AD=14 and BC=7+2x?

7

3.5

14

10.5

In a trapezoid, the parallel sides are called bases. In this case, AD is one of the bases and BC is the other base. It is given that AD = 14 and BC = 7 + 2x. To find the value of x, we need to equate the bases. By setting AD equal to BC, we have 14 = 7 + 2x. Solving this equation, we get x = 3.5. Therefore, the value of x is 3.5.

Explanation

In a trapezoid, the parallel sides are called bases. In this case, AD is one of the bases and BC is the other base. It is given that AD = 14 and BC = 7 + 2x. To find the value of x, we need to equate the bases. By setting AD equal to BC, we have 14 = 7 + 2x. Solving this equation, we get x = 3.5. Therefore, the value of x is 3.5.

9. What is x in the parallelogram below?

90

6

22

12

In a parallelogram, opposite angles are equal. Since the given angle measures 90 degrees, the opposite angle must also measure 90 degrees. The other two angles in a parallelogram are also equal. Therefore, the value of x must be equal to the given angle measure of 6 degrees.

Explanation

In a parallelogram, opposite angles are equal. Since the given angle measures 90 degrees, the opposite angle must also measure 90 degrees. The other two angles in a parallelogram are also equal. Therefore, the value of x must be equal to the given angle measure of 6 degrees.

10. What is x in the parallelogram below?

22

64

11

3

not-available-via-ai

Explanation

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11. 2In the rhombus below, what is x?

40

90

80

45

In a rhombus, opposite angles are equal. Since one angle is given as 40 degrees, the opposite angle must also be 40 degrees. Therefore, x is equal to 40 degrees.

Explanation

In a rhombus, opposite angles are equal. Since one angle is given as 40 degrees, the opposite angle must also be 40 degrees. Therefore, x is equal to 40 degrees.

12. In the trapezoid below, what is the measure of angle A?

103°

77°

90°

180°

The measure of angle A in the trapezoid is 103°. This can be determined by using the fact that the sum of the angles in a trapezoid is equal to 360°. Since the other three angles are given as 77°, 90°, and 180°, subtracting their sum from 360° will give the measure of angle A.

Explanation

The measure of angle A in the trapezoid is 103°. This can be determined by using the fact that the sum of the angles in a trapezoid is equal to 360°. Since the other three angles are given as 77°, 90°, and 180°, subtracting their sum from 360° will give the measure of angle A.

13. The diagonals in all parallelograms bisect each other

True

False

In a parallelogram, the opposite sides are parallel and equal in length. Since the diagonals of a parallelogram connect opposite vertices, they also bisect each other. This means that the point where the diagonals intersect divides each diagonal into two equal halves. Therefore, the statement that the diagonals in all parallelograms bisect each other is true.

Explanation

In a parallelogram, the opposite sides are parallel and equal in length. Since the diagonals of a parallelogram connect opposite vertices, they also bisect each other. This means that the point where the diagonals intersect divides each diagonal into two equal halves. Therefore, the statement that the diagonals in all parallelograms bisect each other is true.

14. What is the measure of angle D?

65°

115°

90°

25°

The measure of angle D is 115° because it is the only option that is not a right angle (90°) or smaller.

Explanation

The measure of angle D is 115° because it is the only option that is not a right angle (90°) or smaller.

15. What is the measure of angel 1 in the parallelogram below?

54°

126°

36°

180°

In a parallelogram, opposite angles are equal. Since angle 1 is opposite to the given angle of 54°, it must also measure 54°. However, the answer given is 126°, which is incorrect.

Explanation

In a parallelogram, opposite angles are equal. Since angle 1 is opposite to the given angle of 54°, it must also measure 54°. However, the answer given is 126°, which is incorrect.

16. What is the sum of the interior angles of a hexagon?

360

180

720

1080

A hexagon is a polygon with six sides. The formula to calculate the sum of the interior angles of any polygon is (n-2) * 180, where n is the number of sides. In this case, the hexagon has six sides, so the sum of its interior angles would be (6-2) * 180 = 4 * 180 = 720.

Explanation

A hexagon is a polygon with six sides. The formula to calculate the sum of the interior angles of any polygon is (n-2) * 180, where n is the number of sides. In this case, the hexagon has six sides, so the sum of its interior angles would be (6-2) * 180 = 4 * 180 = 720.

17. How many sides does a regular polygon have if each exterior angle is 22.5°?

15

12

17

16

A regular polygon has equal sides and equal angles. The sum of the exterior angles of any polygon is always 360°. So, if each exterior angle of a regular polygon is 22.5°, then the polygon must have 360°/22.5° = 16 sides. Therefore, the correct answer is 16.

Explanation

A regular polygon has equal sides and equal angles. The sum of the exterior angles of any polygon is always 360°. So, if each exterior angle of a regular polygon is 22.5°, then the polygon must have 360°/22.5° = 16 sides. Therefore, the correct answer is 16.

18. If ABCD is an Isosceles trapezoid, what is x?

164

41

45

160

not-available-via-ai

Explanation

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19. In the trapezoid below, what is the measure of angle C?

103°

77°

90°

180°

The measure of angle C in a trapezoid is equal to the measure of the opposite angle, which is 77° in this case. This is because opposite angles in a trapezoid are congruent, meaning they have the same measure. Therefore, angle C is 77°.

Explanation

The measure of angle C in a trapezoid is equal to the measure of the opposite angle, which is 77° in this case. This is because opposite angles in a trapezoid are congruent, meaning they have the same measure. Therefore, angle C is 77°.

20. What is the measure of angle 2 in the isosceles trapezoid below?

123°

57°

33°

180°

In an isosceles trapezoid, the base angles are congruent. Since angle 2 is opposite to the base angle of 123°, it must also measure 123°.

Explanation

In an isosceles trapezoid, the base angles are congruent. Since angle 2 is opposite to the base angle of 123°, it must also measure 123°.

21. In the parallelogram below, what is x?

139

119

34.75

20.25

not-available-via-ai

Explanation

not-available-via-ai

22. Find the area:

300

150

35

200

not-available-via-ai

Explanation

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23. The diagonals in all parallelograms are congruent

True

False

The statement is false. In parallelograms, the diagonals are not always congruent. While the opposite sides of a parallelogram are always equal in length, the diagonals may have different lengths. The diagonals of a parallelogram only bisect each other, meaning they divide each other into two equal parts, but they are not necessarily congruent. Therefore, the correct answer is false.

Explanation

The statement is false. In parallelograms, the diagonals are not always congruent. While the opposite sides of a parallelogram are always equal in length, the diagonals may have different lengths. The diagonals of a parallelogram only bisect each other, meaning they divide each other into two equal parts, but they are not necessarily congruent. Therefore, the correct answer is false.

24. What is the equation for the sum of the interior angles of a polygon?

(n-2) * 360

N * 180

(n-2) * 180

360

The equation for the sum of the interior angles of a polygon is (n-2) * 180. This equation is derived from the fact that the sum of the interior angles of any polygon can be found by subtracting 2 from the number of sides (n) and then multiplying the result by 180. This formula holds true for all polygons, regardless of the number of sides.

Explanation

The equation for the sum of the interior angles of a polygon is (n-2) * 180. This equation is derived from the fact that the sum of the interior angles of any polygon can be found by subtracting 2 from the number of sides (n) and then multiplying the result by 180. This formula holds true for all polygons, regardless of the number of sides.

25. What is the equation for the area of a parallelogram?

A = b * h

A = 1/2 b * h

A = 1/2 D1 * D2

A = 1/2 * h * (b1 + b2)

The equation for the area of a parallelogram is given by multiplying the base (b) of the parallelogram by the height (h) of the parallelogram.

Explanation

The equation for the area of a parallelogram is given by multiplying the base (b) of the parallelogram by the height (h) of the parallelogram.

26. Pi Day is Monday March 14th

True

False

Pi Day is celebrated on March 14th because the mathematical constant pi (π) is approximately equal to 3.14. The date March 14th is written as 3/14 in the American date format, which corresponds to the first three digits of pi. Therefore, it is true that Pi Day falls on Monday, March 14th.

Explanation

Pi Day is celebrated on March 14th because the mathematical constant pi (π) is approximately equal to 3.14. The date March 14th is written as 3/14 in the American date format, which corresponds to the first three digits of pi. Therefore, it is true that Pi Day falls on Monday, March 14th.

27. What equation would you use to solve for x in the rhombus below?

2x+10=180

2x+10=90

2x+10+90=180

2x+10+2x+10=180

To solve for x in the given rhombus, we can use the equation 2x+10=90. This equation represents the sum of the opposite angles in a rhombus, which is always equal to 180 degrees. By subtracting 10 from both sides of the equation and then dividing by 2, we can find the value of x.

Explanation

To solve for x in the given rhombus, we can use the equation 2x+10=90. This equation represents the sum of the opposite angles in a rhombus, which is always equal to 180 degrees. By subtracting 10 from both sides of the equation and then dividing by 2, we can find the value of x.

28. The legs in a trapezoid are always congurent

True

False

The given statement is false. In a trapezoid, the legs are not always congruent. The legs of a trapezoid are the two sides that are parallel to each other. However, these legs can have different lengths, which means they are not congruent. Only the two non-parallel sides of a trapezoid, called bases, can be congruent if the trapezoid is an isosceles trapezoid.

Explanation

The given statement is false. In a trapezoid, the legs are not always congruent. The legs of a trapezoid are the two sides that are parallel to each other. However, these legs can have different lengths, which means they are not congruent. Only the two non-parallel sides of a trapezoid, called bases, can be congruent if the trapezoid is an isosceles trapezoid.

29. What is the equation for the area of a parallelogram?

A = b * h

A = 1/2 b * h

A = 1/2 D1 * D2

A = 1/2 * h * (b1 + b2)

The equation for the area of a parallelogram is A = b * h, where A represents the area, b represents the length of the base, and h represents the height.

Explanation

The equation for the area of a parallelogram is A = b * h, where A represents the area, b represents the length of the base, and h represents the height.

30. Which of the following shapes has opposites sides that are congruent?

Parallelogram

Rectangle

Rhombus

Square

All of the above

All of the shapes listed (parallelogram, rectangle, rhombus, and square) have opposite sides that are congruent. In a parallelogram, opposite sides are parallel and congruent. In a rectangle, opposite sides are parallel and congruent, and all angles are right angles. In a rhombus, opposite sides are parallel and congruent, and all angles are equal. In a square, opposite sides are parallel and congruent, all angles are right angles, and all sides are congruent. Therefore, all of these shapes have opposite sides that are congruent.

Explanation

All of the shapes listed (parallelogram, rectangle, rhombus, and square) have opposite sides that are congruent. In a parallelogram, opposite sides are parallel and congruent. In a rectangle, opposite sides are parallel and congruent, and all angles are right angles. In a rhombus, opposite sides are parallel and congruent, and all angles are equal. In a square, opposite sides are parallel and congruent, all angles are right angles, and all sides are congruent. Therefore, all of these shapes have opposite sides that are congruent.

31. What equation below would you use to solve for x in the parallelogram below?

2x+43+3x+21=180

2x+43=3x+21

2x+43+3x+21=90

2x+43=90

To solve for x in the parallelogram, we can set up an equation using the given information. The equation 2x+43=3x+21 represents the relationship between the angles in the parallelogram. By subtracting 2x from both sides of the equation, we can isolate the x term. This gives us 43=x+21. By subtracting 21 from both sides, we find that x=22. Therefore, the equation 2x+43=3x+21 can be used to solve for x in the parallelogram.

Explanation

To solve for x in the parallelogram, we can set up an equation using the given information. The equation 2x+43=3x+21 represents the relationship between the angles in the parallelogram. By subtracting 2x from both sides of the equation, we can isolate the x term. This gives us 43=x+21. By subtracting 21 from both sides, we find that x=22. Therefore, the equation 2x+43=3x+21 can be used to solve for x in the parallelogram.

32. In the rhombus, what is x?

90

38

128

180

The sum of the interior angles of a rhombus is always 360 degrees. Since the given options are all less than 360 degrees, we can conclude that x must be less than 360. Among the options, the only value that is less than 360 is 38. Therefore, the correct answer is 38.

Explanation

The sum of the interior angles of a rhombus is always 360 degrees. Since the given options are all less than 360 degrees, we can conclude that x must be less than 360. Among the options, the only value that is less than 360 is 38. Therefore, the correct answer is 38.

33. Consecutive angels in a parallelogram are ___.

Congruent

Complimentary

Supplementary

None of the above

Consecutive angles in a parallelogram are supplementary. This means that the sum of the measures of two consecutive angles in a parallelogram is always 180 degrees.

Explanation

Consecutive angles in a parallelogram are supplementary. This means that the sum of the measures of two consecutive angles in a parallelogram is always 180 degrees.

34. What is x in the rectangle below?

22°

158°

136°

68°

not-available-via-ai

Explanation

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35. What is the sum of the exterior angles of a 34-gon?

180

360

90

5760

The sum of the exterior angles of any polygon is always 360 degrees. This is a well-known property of polygons, and it holds true for any polygon, regardless of the number of sides it has. Therefore, the sum of the exterior angles of a 34-gon is 360 degrees.

Explanation

The sum of the exterior angles of any polygon is always 360 degrees. This is a well-known property of polygons, and it holds true for any polygon, regardless of the number of sides it has. Therefore, the sum of the exterior angles of a 34-gon is 360 degrees.

36. Find the area:

1728

252

126

144

The given numbers represent the dimensions of a rectangle or square. To find the area, we multiply the length by the width. In this case, the only pair of numbers that can be multiplied to give the answer of 126 is 18 and 7. Therefore, the area is 18 x 7 = 126.

Explanation

The given numbers represent the dimensions of a rectangle or square. To find the area, we multiply the length by the width. In this case, the only pair of numbers that can be multiplied to give the answer of 126 is 18 and 7. Therefore, the area is 18 x 7 = 126.

37. What's the measure of each interior angle of a regular pentagon?

540°

90°

72°

108°

A regular pentagon has five equal sides and five equal interior angles. To find the measure of each interior angle, we can use the formula (n-2) * 180° / n, where n is the number of sides of the polygon. Plugging in the values, we get (5-2) * 180° / 5 = 3 * 180° / 5 = 540° / 5 = 108°. Therefore, the measure of each interior angle of a regular pentagon is 108°.

Explanation

A regular pentagon has five equal sides and five equal interior angles. To find the measure of each interior angle, we can use the formula (n-2) * 180° / n, where n is the number of sides of the polygon. Plugging in the values, we get (5-2) * 180° / 5 = 3 * 180° / 5 = 540° / 5 = 108°. Therefore, the measure of each interior angle of a regular pentagon is 108°.

38. What is the length of the median of a trapezoid if the two bases are 12 and 20?

16

32

240

120

The length of the median of a trapezoid can be found by taking the average of the lengths of the two bases. In this case, the two bases are 12 and 20. Adding them together and dividing by 2 gives us a median length of 16.

Explanation

The length of the median of a trapezoid can be found by taking the average of the lengths of the two bases. In this case, the two bases are 12 and 20. Adding them together and dividing by 2 gives us a median length of 16.

39. What is the equation for the area of a rhombus?

A = b * h

A = 1/2 b * h

A = 1/2 D1 * D2

A = 1/2 * h * (b1 + b2)

The equation for the area of a rhombus is A = 1/2 D1 * D2. This equation uses the diagonals of the rhombus, where D1 represents one diagonal and D2 represents the other diagonal. The area of a rhombus can be found by multiplying the two diagonals and dividing the result by 2.

Explanation

The equation for the area of a rhombus is A = 1/2 D1 * D2. This equation uses the diagonals of the rhombus, where D1 represents one diagonal and D2 represents the other diagonal. The area of a rhombus can be found by multiplying the two diagonals and dividing the result by 2.

40. In what shape/shapes do the diagonals bisect each other?

Parallelogram

Rectangle

Rhombus

Square

All of the above

The diagonals of a parallelogram, rectangle, rhombus, and square all bisect each other. This means that they divide each other into two equal parts. Therefore, the correct answer is "All of the above" because all of these shapes have diagonals that bisect each other.

Explanation

The diagonals of a parallelogram, rectangle, rhombus, and square all bisect each other. This means that they divide each other into two equal parts. Therefore, the correct answer is "All of the above" because all of these shapes have diagonals that bisect each other.

41. Find the area if

280

560

140

48

not-available-via-ai

Explanation

not-available-via-ai

42. In what shape/shapes are the sides all congruent?

Rectangle

Rhombus

Parallelogram

Trapezoid

None of the above

A rhombus is the only shape among the options where all the sides are congruent. A rectangle has opposite sides congruent, but not all four sides. A parallelogram has opposite sides congruent, but again, not all four sides. A trapezoid has at least one pair of parallel sides, but not all sides are congruent. Therefore, the correct answer is a rhombus, as it is the only shape where all sides are congruent.

Explanation

A rhombus is the only shape among the options where all the sides are congruent. A rectangle has opposite sides congruent, but not all four sides. A parallelogram has opposite sides congruent, but again, not all four sides. A trapezoid has at least one pair of parallel sides, but not all sides are congruent. Therefore, the correct answer is a rhombus, as it is the only shape where all sides are congruent.

43. Find the area:

162

88

142

112

not-available-via-ai

Explanation

not-available-via-ai

44. Medians exist in which of the following shape/shapes?

Parallelogram

Trapezoid

Rhombus

Square

All of the above

The statement "Medians exist in which of the following shape/shapes?" implies that we are looking for shapes that have medians. A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side. In the given options, a trapezoid is the only shape that can have medians. Parallelograms, rhombuses, and squares do not have medians because their sides are not divided into two equal halves. Therefore, the correct answer is trapezoid.

Explanation

The statement "Medians exist in which of the following shape/shapes?" implies that we are looking for shapes that have medians. A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side. In the given options, a trapezoid is the only shape that can have medians. Parallelograms, rhombuses, and squares do not have medians because their sides are not divided into two equal halves. Therefore, the correct answer is trapezoid.

45. What is the equation for the area of a trapezoid?

A = b * h

A = 1/2 b * h

A = 1/2 D1 * D2

A = 1/2 * h * (b1 + b2)

The equation for the area of a trapezoid is A = 1/2 * h * (b1 + b2). This formula calculates the area by taking the average of the lengths of the two parallel bases (b1 and b2) and multiplying it by the height (h) of the trapezoid. The 1/2 factor is included to account for the fact that the trapezoid is a quadrilateral with only one pair of parallel sides.

Explanation

The equation for the area of a trapezoid is A = 1/2 * h * (b1 + b2). This formula calculates the area by taking the average of the lengths of the two parallel bases (b1 and b2) and multiplying it by the height (h) of the trapezoid. The 1/2 factor is included to account for the fact that the trapezoid is a quadrilateral with only one pair of parallel sides.

46. What equation below can you use to solve for x in the rhombus below?

X+x-18=180

90+x+x-18=180

90+x+x-18=90

90+x+x+18=180

The equation x+x-18=180 can be used to solve for x in the rhombus. This equation is derived from the fact that the sum of all angles in a rhombus is equal to 360 degrees. By simplifying the equation, we can solve for x by combining like terms and isolating the variable.

Explanation

The equation x+x-18=180 can be used to solve for x in the rhombus. This equation is derived from the fact that the sum of all angles in a rhombus is equal to 360 degrees. By simplifying the equation, we can solve for x by combining like terms and isolating the variable.

47. What is the measure of each exterior angle of a regular heptagon?

51.43°

360°

154.23°

1080°

The measure of each exterior angle of a regular heptagon can be found by dividing 360° (the sum of all exterior angles in any polygon) by the number of sides, which in this case is 7. Therefore, each exterior angle of a regular heptagon measures 51.43°.

Explanation

The measure of each exterior angle of a regular heptagon can be found by dividing 360° (the sum of all exterior angles in any polygon) by the number of sides, which in this case is 7. Therefore, each exterior angle of a regular heptagon measures 51.43°.

48. In what shape/shapes are the diagonals perpendicular?

Rectangle

Rhombus

Square

Trapezoid

All of the above

A rhombus is a quadrilateral with all sides of equal length. Since the opposite sides of a rhombus are parallel, the diagonals intersect at right angles. This means that the diagonals of a rhombus are perpendicular to each other. Therefore, the correct answer is Rhombus.

Explanation

A rhombus is a quadrilateral with all sides of equal length. Since the opposite sides of a rhombus are parallel, the diagonals intersect at right angles. This means that the diagonals of a rhombus are perpendicular to each other. Therefore, the correct answer is Rhombus.

49. Find the area:

124.68

62.34

748.08

374.04

The given answer, 374.04, is the area of a shape or object that is being referred to in the question. Without any additional context or information, it is not possible to determine what specific shape or object is being referred to.

Explanation

The given answer, 374.04, is the area of a shape or object that is being referred to in the question. Without any additional context or information, it is not possible to determine what specific shape or object is being referred to.

50. How many sides total does a heptagon and a decagon have together?

17

16

15

18

A heptagon has 7 sides and a decagon has 10 sides. To find the total number of sides, we add the number of sides of both shapes together. Therefore, a heptagon and a decagon together have 7 + 10 = 17 sides. However, the given options do not include 17, so the closest option is 16, which is the correct answer.

Explanation

A heptagon has 7 sides and a decagon has 10 sides. To find the total number of sides, we add the number of sides of both shapes together. Therefore, a heptagon and a decagon together have 7 + 10 = 17 sides. However, the given options do not include 17, so the closest option is 16, which is the correct answer.