Deck 5: Quadrilaterals

Question 1

If sides and of quadrilateral MNPQ are congruent and also parallel, then MNPQ is a parallelogram.

Answer 1

False

Question 2

If in , then is an altitude of with respect to base .

Answer 2

False

Question 3

Leaving home, the driver of a car travels 10 miles in the direction N 53° E. In what direction must the driver travel to return home?

A)S 37 ° W
B)N 37 ° W
C)S 53 ° W
D)None of These

Answer 3

C

Question 4

How are the diagonals of any parallelogram related?

A)congruent
B)perpendicular
C)bisect each other
D)None of These

Question 5

For , E lies on side so that . For , what name is given to the line segment ?

Question 6

For a parallelogram to be a rhombus, what condition must it satisfy?

Question 7

The diagonals of quadrilateral MNPQ are perpendicular-bisectors of each other. Being as specific as possible, what type of quadrilateral is MNPQ?

A)parallelogram
B)rectangle
C)square
D)rhombus

Question 8

Given , name an angle that is supplementary to .

Question 9

In , and are supplementary.

Question 10

The diagonals of any rectangle are both perpendicular and congruent.

Question 11

Both pairs of opposite sides of quadrilateral WXYZ are congruent. Being as specific as possible, what type of quadrilateral is WXYZ?

A)parallelogram
B)rectangle
C)square
D)rhombus

Question 12

The bearing of the airplane with the path shown is N 30° E.

Question 13

A diagonal of a parallelogram separates the parallelogram into two congruent triangles.

Question 14

Consider . If the midpoints of the sides are joined in order, the resulting quadrilateral must be a:

A)parallelogram
B)rectangle
C)kite
D)trapezoid

Question 15

For every parallelogram, two adjacent sides must be congruent.

Question 16

The diagonals of a quadrilateral ABCD are shown. If and bisect each other, what type of quadrilateral is ABCD ? Be as specific as possible.

Question 17

What relationship exists among the sides of a skew quadrilateral?

Question 18

For (not shown), it follows that:

A)
B)
C)
D) and are supplementary.

Question 19

When the midpoints of the sides of a kite RSTV are joined in order, quadrilateral MNPQ is formed. Being as specific as possible, what type of quadrilateral is MNPQ?

Question 20

For , is an altitude with respect to base . In relation to , what word is used for the length of ?

Question 21

In kite WXYZ , WX = WZ and XY = YZ . If and m = 76 ° , find m .

Question 22

In , M is the midpoint of and N is the midpoint of . If the length of is represented by , what expression (containing x )represents the length of ?

Question 23

In kite ABCD , . It follows that:

A)
B)
C)
D)

Question 24

In kite ABCD , and . Diagonals and intersect at point E . If AC = 18.6 and BD = 9.2, find the length of .

Question 25

If M and N are midpoints of sides and of , then .

Question 26

If M and N are the midpoints of sides and of , then .

Question 27

In , m is 26 ° larger than m . Find m .

A)77 °
B)103 °
C)116 °
D)126 °

Question 28

For , m = 103 ° and it follows that is the longer diagonal.

Question 29

If and , then .

Question 30

In , M and N are the midpoints of and as shown. Then:

A)
B)
C)
D)None of These

Question 31

For , M and N are the midpoints of the indicated sides. If and , find the length of .

Question 32

is an altitude for . If RV = 5, RS = 7, and WT = 4, find the length of altitude .

A)3
B)3.5
C)4
D)None of These

Question 33

Both the kite and the parallelogram have two pairs of congruent angles.

Question 34

If the midpoints of the sides of are joined to form , then the perimeter of will be twice that of .

Question 35

For kite MNPQ , and . If diagonal is drawn, what type of triangles are formed?

Question 36

In , RT = 12, ST = 14, and RS = 16. Where M is the midpoint of and N is the midpoint of , find the perimeter of .

Question 37

In , AB = 5.7 cm and BC = 8.2 cm. What is the perimeter of ?

Question 38

In kite MNPQ , . For this kite, name another pair of congruent sides.

Question 39

In rhombus MNPQ , diagonal is congruent to side . Find m .

Question 40

For , points M , N , and P are the midpoints of the sides. If the perimeter of is 47 inches, find the perimeter of .

A)23 inches
B)23.5 inches
C)47 inches
D)None of These

Question 41

For a quadrilateral to be a rectangle, how must the diagonals be related?

A)perpendicular
B)congruent
C)bisect each other
D)congruent and bisect each other

Question 42

When the midpoints of the sides of a quadrilateral are joined in order, the quadrilateral formed is always a square.

Question 43

The diagonals of any rhombus are perpendicular.

Question 44

In addition to being congruent, how are the diagonals of a square related?

Question 45

When the midpoints of the sides of a square RSTV are joined in order, quadrilateral MNPQ is formed. Being as specific as possible, what type of quadrilateral is MNPQ?

Question 46

If the diagonals of a rhombus have lengths 6 and 8, then the perimeter of the rhombus is 28.

Question 47

If the diagonals of a rhombus measure 10 cm and 24 cm, what is the perimeter of the rhombus?

A)13 cm
B)34 cm
C)52 cm
D)68 cm

Question 48

In quadrilateral WXYZ , . If and , determine a value of x so that WXYZ must be a parallelogram.

Question 49

The midpoints of the sides of rhombus ABCD are joined in order to form quadrilateral MNPQ. Being as specific as possible, what type of quadrilateral is MNPQ?

A)parallelogram
B)rectangle
C)square
D)rhombus

Question 50

For a quadrilateral to be "cyclic," what requirement must be satisfied?

Question 51

In , m and m . Determine the value of x .

Question 52

In rectangle ABCD , AB = 5 and BC = 4. As a square root, find the length of diagonal .

Question 53

For rhombus RSTV , diagonals and intersect at point W . If RT = 16 and VS = 12, find the length of each side of rhombus RSTV .

Question 54

In , RS = 19, ST = 15, and WT = 10. Find the length of altitude .

Question 55

The driver of an automobile leaves home and travels due east 8 miles. Turning right at an intersection, he drives due south a distance of 6 miles. How far is the driver from home?

Question 56

In , , , and . Find the length of side .

Question 57

If AB = 3 and BC = 4 in rectangle ABCD , then the length of diagonal is 5.

Question 58

In kite ABCD , AB = AD = y 5, BC = y , and . Find the perimeter of ABCD .

Question 59

In , diagonals and intersect at point T . If MN = 12.5, NP = 8.7, and QN = 14.6, find QT .

Question 60

If the diagonals of a quadrilateral are perpendicular, the quadrilateral must be a square.

Question 61

If the diagonals of a quadrilateral are perpendicular, the quadrilateral must be a square.

Question 62

In rectangle ABCD , AB = 5 and BC = 4. As a square root, find the length of diagonal .

Question 63

For a quadrilateral to be a rectangle, how must the diagonals be related?

A)perpendicular
B)congruent
C)bisect each other
D)congruent and bisect each other

Question 64

When the midpoints of the sides of a quadrilateral are joined in order, the quadrilateral formed is always a square.

Question 65

If the diagonals of a rhombus measure 10 cm and 24 cm, what is the perimeter of the rhombus?

A)13 cm
B)34 cm
C)52 cm
D)68 cm

Question 66

The midpoints of the sides of rhombus ABCD are joined in order to form quadrilateral MNPQ. Being as specific as possible, what type of quadrilateral is MNPQ?

A)parallelogram
B)rectangle
C)square
D)rhombus

Question 67

In rhombus MNPQ , diagonal is congruent to side . Find m .

Question 68

If the diagonals of a rhombus have lengths 6 and 8, then the perimeter of the rhombus is 28.

Question 69

Given kite ABCD with and , the diagonals (if drawn)would be perpendicular. For diagonals and , what other relationship exists?

Question 70

In addition to being congruent, how are the diagonals of a square related?

Question 71

The driver of an automobile leaves home and travels due east 8 miles. Turning right at an intersection, he drives due south a distance of 6 miles. How far is the driver from home?

Question 72

For trapezoid RSTV , , and is the median. If RS = 6.5, ST = 8.5, VT = 14.7, and VR = 9.7, then the length of is:

A)10.6
B)15.0
C)9.1
D)21.2

Question 73

In isosceles trapezoid HJKL , . Suppose that points M , N , P , and Q are the midpoints of the sides , , , and respectively. If the length of diagonal is 10 cm, find the perimeter of MNPQ .

Question 74

The diagonals of any rhombus are perpendicular.

Question 75

For rhombus RSTV , diagonals and intersect at point W . If RT = 16 and VS = 12, find the length of each side of rhombus RSTV .

Question 76

For trapezoid RSTV , . If M is the midpoint of and N is the midpoint of , it follows that:

A) , , and
B) , ,and
C) and
D) , , and

Question 77

In , m and m . Find the value of x .

Question 78

When the midpoints of the sides of a square RSTV are joined in order, quadrilateral MNPQ is formed. Being as specific as possible, what type of quadrilateral is MNPQ?

Question 79

For a quadrilateral to be "cyclic," what requirement must be satisfied?

Question 80

If AB = 3 and BC = 4 in rectangle ABCD , then the length of diagonal is 5.