AnswersMASTER COURSE GeometrySpecial Parallelograms

Special Parallelograms — Quiz Answers

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1
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Is the figure a rectangle? Explain.

A
Yes, it is a rectangle because the diagonals are congruent.
B
Yes, it is a rectangle because the sides of the parallelogram do meet at right angles.
C
No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.
D
No, it is not a rectangle because the diagonals are congruent.
2
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Which equation is true regarding the angles formed by the diagonals and sides of the rhombus?

A
2 x plus 2 y is equal to 4 z
B
x plus y is equal to z
C
z plus x is equal to 2 y
D
2 x is equal to y plus z
3

If ABCD is also a rhombus, what must be the value of x ?

A
15
B
23
C
13
D
18
4

Which measures are true for the quilt piece? Choose three correct answers.

A
The perimeter of the rhombus is 16 inches.
B
The length of the longer diagonal is approximately 7 inches.
C
x is equal to 3 in.
D
The measure of the greater interior angle of the rhombus is 90 degrees .
E
a is equal to 60 degrees
5

The length of line segment cap l cap n is 28 centimeters. What is the length of line segment cap l cap p ?

A
14 cm
B
7 cm
C
9 cm
D
21 cm
6

Diagonals line segment cap A cap c and line segment cap b cap d form right angles at point cap m in parallelogram cap A cap b cap c cap d Prove cap A cap b cap c cap d is a rhombus. Which is the missing statement in step 6 ? Expand Image

A
triangle cap A cap m cap b is congruent to triangle cap c cap m cap d comma triangle cap c cap m cap d is congruent to triangle cap b cap A cap d comma triangle cap b cap A cap d is congruent to triangle cap b cap c cap d
B
triangle cap A cap b cap c is congruent to triangle cap A cap d cap c comma triangle cap A cap d cap c is congruent to triangle cap b cap A cap d comma triangle cap b cap A cap d is congruent to triangle cap b cap c cap d
C
triangle cap A cap m cap b is congruent to triangle cap c cap m cap b comma triangle cap c cap m cap b is congruent to triangle cap c cap m cap d comma triangle cap c cap m cap d is congruent to triangle cap A cap m cap d
D
triangle cap A cap b cap c is congruent to triangle cap A cap d cap c comma triangle cap A cap d cap c is congruent to triangle cap A cap m cap d comma triangle cap A cap m cap d is congruent to triangle cap b cap m cap c
7

Which statements are true of all squares? Choose three correct answers.

A
The diagonals are congruent to the sides of the square.
B
The diagonals are twice the length of one side of the square.
C
The diagonals are perpendicular.
D
The diagonals bisect the vertex angles.
E
The diagonals are congruent to each other.
8

A square has a diagonal measuring 6⁢sqrt(2) inches. What is the perimeter of the square? Enter your answer in the box.

Answer:

24

9

A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal?

A
39 units
B
49 units
C
41 units
D
31 units
10

What type of triangle is triangle cap s cap t cap r ?

A
scalene triangle
B
right triangle
C
equilateral triangle
D
isosceles triangle
11

If ABCD is also a rhombus, what must be the value of x ?

A
13
B
18
C
15
D
23
12

Diagonals line segment cap A cap c and line segment cap b cap d form right angles at point cap m in parallelogram cap A cap b cap c cap d Prove cap A cap b cap c cap d is a rhombus. Which is the missing statement in step 6 ? Expand Image

A
triangle cap A cap b cap c is congruent to triangle cap A cap d cap c comma triangle cap A cap d cap c is congruent to triangle cap b cap A cap d comma triangle cap b cap A cap d is congruent to triangle cap b cap c cap d
B
triangle cap A cap b cap c is congruent to triangle cap A cap d cap c comma triangle cap A cap d cap c is congruent to triangle cap A cap m cap d comma triangle cap A cap m cap d is congruent to triangle cap b cap m cap c
C
triangle cap A cap m cap b is congruent to triangle cap c cap m cap b comma triangle cap c cap m cap b is congruent to triangle cap c cap m cap d comma triangle cap c cap m cap d is congruent to triangle cap A cap m cap d
D
triangle cap A cap m cap b is congruent to triangle cap c cap m cap d comma triangle cap c cap m cap d is congruent to triangle cap b cap A cap d comma triangle cap b cap A cap d is congruent to triangle cap b cap c cap d
13

What type of triangle is triangle cap s cap t cap r ?

A
equilateral triangle
B
isosceles triangle
C
scalene triangle
D
right triangle
14

Is the figure a rectangle? Explain.

A
Yes, it is a rectangle because the sides of the parallelogram do meet at right angles.
B
No, it is not a rectangle because the diagonals are congruent.
C
No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.
D
Yes, it is a rectangle because the diagonals are congruent.
15

Is the figure a rectangle? Explain.

A
Yes, it is a rectangle because the sides of the parallelogram do meet at right angles.
B
No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.
C
No, it is not a rectangle because the diagonals are congruent.
D
Yes, it is a rectangle because the diagonals are congruent.
16

Diagonals line segment cap A cap c and line segment cap b cap d form right angles at point cap m in parallelogram cap A cap b cap c cap d Prove cap A cap b cap c cap d is a rhombus. Which is the missing statement in step 6 ? Expand Image

A
triangle cap A cap m cap b is congruent to triangle cap c cap m cap b comma triangle cap c cap m cap b is congruent to triangle cap c cap m cap d comma triangle cap c cap m cap d is congruent to triangle cap A cap m cap d
B
triangle cap A cap b cap c is congruent to triangle cap A cap d cap c comma triangle cap A cap d cap c is congruent to triangle cap b cap A cap d comma triangle cap b cap A cap d is congruent to triangle cap b cap c cap d
C
triangle cap A cap b cap c is congruent to triangle cap A cap d cap c comma triangle cap A cap d cap c is congruent to triangle cap A cap m cap d comma triangle cap A cap m cap d is congruent to triangle cap b cap m cap c
D
triangle cap A cap m cap b is congruent to triangle cap c cap m cap d comma triangle cap c cap m cap d is congruent to triangle cap b cap A cap d comma triangle cap b cap A cap d is congruent to triangle cap b cap c cap d
17

Diagonals line segment cap A cap c and line segment cap b cap d form right angles at point cap m in parallelogram cap A cap b cap c cap d Prove cap A cap b cap c cap d is a rhombus. Which is the missing statement in step 6 ? Expand Image

A
triangle cap A cap m cap b is congruent to triangle cap c cap m cap d comma triangle cap c cap m cap d is congruent to triangle cap b cap A cap d comma triangle cap b cap A cap d is congruent to triangle cap b cap c cap d
B
triangle cap A cap b cap c is congruent to triangle cap A cap d cap c comma triangle cap A cap d cap c is congruent to triangle cap A cap m cap d comma triangle cap A cap m cap d is congruent to triangle cap b cap m cap c
C
triangle cap A cap b cap c is congruent to triangle cap A cap d cap c comma triangle cap A cap d cap c is congruent to triangle cap b cap A cap d comma triangle cap b cap A cap d is congruent to triangle cap b cap c cap d
D
triangle cap A cap m cap b is congruent to triangle cap c cap m cap b comma triangle cap c cap m cap b is congruent to triangle cap c cap m cap d comma triangle cap c cap m cap d is congruent to triangle cap A cap m cap d
18

If ABCD is also a rhombus, what must be the value of x ?

A
13
B
18
C
23
D
15
19

Is the figure a rectangle? Explain.

A
No, it is not a rectangle because the diagonals are congruent.
B
Yes, it is a rectangle because the diagonals are congruent.
C
Yes, it is a rectangle because the sides of the parallelogram do meet at right angles.
D
No, it is not a rectangle because the sides of the parallelogram do not meet at right angles.
20

The length of line segment cap l cap n is 28 centimeters. What is the length of line segment cap l cap p ?

A
14 cm
B
7 cm
C
9 cm
D
21 cm

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