Question 1

In parallelogram ABCD, m<1 = 45˚ and m<DCB = 120˚.  What is m<2?

Accepted Answer

15

Answer

30

Answer

45

Answer

60

Question 2

A quadrilateral whose diagonals bisect each other and are perpendicular is always a

Accepted Answer

rhombus

Answer

rectangle

Answer

trapezoid

Answer

parallelogram

Question 3

The diagonals of a quadrilateral are congruent but do not bisect each other. This quadrilateral is

Accepted Answer

an isosceles trapezoid

Answer

a rhombus

Answer

a parallelogram

Answer

a rectangle

Question 4

Given three distinct quadrilaterals, a square, a rectangle, and a rhombus, which quadrilaterals must have perpendicular diagonals?

Accepted Answer

the rhombus and the square

Answer

the rhombus, only

Answer

the rhombus, rectangle, and square

Answer

the rectangle and the square

Question 5

In parallelogram QRST, diagonal QS is drawn. Which statement
must always be true?

Accepted Answer

∆STQ $\cong$∆QRS

Answer

∆STQ is an acute triangle.

Answer

QS = QT

Answer

∆QRS is an isosceles triangle.

Question 6

In quadrilateral ABCD, the diagonals bisect its angles. If the diagonals are not congruent, quadrilateral ABCD must be a

Accepted Answer

rhombus

Answer

trapezoid

Answer

square

Answer

rectangle

Question 7

In the diagram of parallelogram STUV, SV = x + 3, VU = 2x − 1, and TU = 4x − 3. The length of SV is

Accepted Answer

5

Answer

2

Answer

4

Answer

7

Question 8

Which statement is true about every parallelogram?

Accepted Answer

Two pairs of opposite sides are congruent.

Answer

The diagonals are perpendicular to each other.

Answer

The interior angles are all congruent.

Answer

The interior angles are all congruent.

Question 9

In the diagram of rhombus ABCD, m∠C = 100.  What is m<DBC?

Accepted Answer

40

Answer

80

Answer

50

Answer

45

Question 10

In the diagram of rhombus MATH, m∠HAM = 12.  What is m∠AMT?

Accepted Answer

78

Answer

12

Answer

84

Answer

156

Question 11

In the diagram of rectangle ABCD,  if AE = x + 2 and BD = 4x - 16, then the length of AC is

Accepted Answer

24

Answer

6

Answer

12

Answer

10

Question 12

Which quadrilateral does NOT always have congruent diagonals?

Accepted Answer

Rhombus

Answer

Isosceles Trapezoid

Answer

Square

Answer

Rectangle

Question 13

In rhombus ABCD, If AC = 18 and BD = 24, what is the length of one side of the rhombus?

Accepted Answer

15

Answer

24

Answer

18

Answer

30

Question 14

In parallelogram ABCD, which statement is true?

Accepted Answer

∠BAE $\cong$∠DCE

Answer

AB $\cong$BC

Answer

BE $\cong$CE

Answer

∠DAE $\cong$∠CBE

Question 15

If the diagonals of a quadrilateral do NOT bisect each other, then the quadrilateral could be a

Accepted Answer

trapezoid

Answer

rectangle

Answer

square

Answer

rhombus

Question 16

In parallelogram ABCD, which statement is NOT always true?

Accepted Answer

AC $\cong$DB

Answer

∠DAE $\cong$∠BCE

Answer

DE $\cong$EB

Answer

∠DEC $\cong$∠BEA

Question 17

In rhombus ABCD, the diagonals AC and BD intersect at E.
If AE = 5 and BE = 12, what is the length of AB?

Accepted Answer

13

Answer

10

Answer

7

Answer

17

Question 18

Which quadrilateral has diagonals that always bisect its angles and also bisect each other?

Accepted Answer

Rhombus

Answer

Kite

Answer

Rectangle

Answer

Isosceles trapezoid

Question 19

In parallelogram ABCD, which statement is always true?

Accepted Answer

∆AED $\cong$∆CEB

Answer

∆DCE $\cong$∆BCE

Answer

AC $\cong$DB

Answer

∠ABD $\cong$∠CBD

Question 20

What is the perimeter of a rhombus whose diagonals are 16 and 30?

Accepted Answer

68

Answer

60

Answer

17

Answer

92

Question 21

In rhombus ABCD, if AD = 10 and AC = 12, what is the length of DB?

Accepted Answer

16

Answer

8

Answer

$\sqrt{44}$

Answer

$\sqrt{136}$

Question 22

The measures of two consecutive angles of a parallelogram are represented by 2x - 40 and 3x + 10.  What is the value of x?

Accepted Answer

42

Question 23

What is the length of a side of a rhombus whose diagonals have lengths 6 and 8?

Accepted Answer

5

Question 24

The measures of two opposite angles of a parallelogram are represented by 3x + 40 and x + 50.  What is the value of x?

Accepted Answer

5

Question 25

In rhombus ABCD, diagonal BD is drawn.  Which statement is NOT always true?

Accepted Answer

AB $\cong$DB

Answer

<ABD $\cong$<DBC

Answer

<ABD $\cong$<ADB

Answer

AB $\cong$DC

Question 26

A parallelogram must be a rectangle when its

Accepted Answer

diagonals are congruent

Answer

opposite sides are parallel

Answer

opposite sides are congruent

Answer

diagonals are perpendicular

Question 27

In parallelogram FRED, ED is extended to A and AF is drawn such that AF = DF.  If m∠R = 124°, what is m∠AFD?

Accepted Answer

68

Answer

56

Answer

124

Answer

112

Question 28

Quadrilateral ABCD has diagonals AC and BD. Which information
is NOT sufficient to prove ABCD is a parallelogram?

Accepted Answer

AB $\cong$CD and BC || AD

Answer

AB $\cong$CD and BC $\cong$AD

Answer

AB $\cong$CD and AB || CD

Answer

AC and BD bisect each other

Question 29

The diagram shows parallelogram LMNO with diagonal LN, m∠M = 118˚, and
m∠LNO = 22˚.  What is m<NLO?

Accepted Answer

40˚

Question 30

In parallelogram QRST, m∠S = 60°, m∠SRT = 83°, and m∠TWU = 35°, what is m∠WVQ?

Accepted Answer

72

Answer

60

Answer

37

Answer

83

Question 31

In parallelogram ABCD, diagonals AC and BD intersect at E. Which
statement does NOT prove parallelogram ABCD is a rhombus?

Accepted Answer

AC $\cong$DB

Answer

AB $\cong$BC

Answer

AC $\perp$BD

Answer

AC bisects ∠DCB

Question 32

Which information is NOT enough to prove ABCD is a parallelogram?

Accepted Answer

AB

\cong

CD and BC || AD

Answer

AB

\cong

CD and BC

\cong

AD

Answer

AB

\cong

CD and AB || CD

Answer

AB || CD and AD ||BC

Question 33

In the diagram below, ABCD is a parallelogram.  If CE $\cong$BE and m∠D = 112°, what is m∠E?

Accepted Answer

44

Answer

112

Answer

68

Answer

56

Question 34

A parallelogram is always a rectangle if

Accepted Answer

the diagonals are congruent

Answer

the diagonals bisect each other

Answer

the diagonals intersect at right angles

Answer

the opposite angles are congruent

Question 35

In quadrilateral BLUE, BE $\cong$UL.  Which information would be sufficient to prove quadrilateral BLUE is a parallelogram?

Accepted Answer

LU || BE

Answer

BL || EU

Answer

LU $\cong$EU

Answer

BE $\cong$BL

Question 36

ROCK is a parallelogram.  What is m∠KSO?

Accepted Answer

135

Answer

45

Answer

110

Answer

125

Question 37

In rhombus PQRS, PR = 16 and QS = 30.  The perimeter of PQRS is

Accepted Answer

68

Question 38

In parallelogram HAND, which statement is always true?

Accepted Answer

AS = 1/2 AD

Answer

HN = 1/2 AD

Answer

∠HDS $\cong$∠NDS

Answer

∠AHS $\cong$∠ANS

Question 39

A parallelogram must be a rhombus if its diagonals

Accepted Answer

are perpendicular to each other

Answer

do not bisect its angles

Answer

are congruent

Answer

bisect each other

Question 40

What additional information is sufficient to prove that parallelogram ABCD is also a rhombus?

Accepted Answer

AC is perpendicular to BD.

Answer

AB is parallel to CD.

Answer

BD bisects AC.

Answer

AC is congruent to BD.

Question 41

Quadrilateral MATH has both pairs of opposite sides congruent and parallel. Which statement about quadrilateral MATH is always true?

Accepted Answer

∠MAT $\cong$∠MHT

Answer

∠ATH $\cong$∠MHT

Answer

MT $\perp$AH

Answer

MT $\cong$AH

Question 42

In parallelogram ABCD, the bisectors of ∠ABC and ∠DCB meet at E.  If m∠A = 68°, determine and state m∠BEC.

Accepted Answer

90

Question 43

In rhombus VENU, diagonals VN and EU intersect at S. If VN = 12 and EU = 16, what is the perimeter of the rhombus?

Accepted Answer

40

Answer

80

Answer

10

Answer

20

Question 44

Which statement about parallelograms is always true?

Accepted Answer

The diagonals bisect each other.

Answer

The diagonals are perpendicular.

Answer

The diagonals are congruent.

Answer

The diagonals bisect their respective angles.

Question 45

In the diagram, ABCD is a parallelogram and DEFG is a rhombus.  If m∠B = 118° and m∠AHC = 138°, determine and state m∠GFH.

Accepted Answer

20

Question 46

A quadrilateral must be a parallelogram if

Accepted Answer

one pair of sides is both parallel and congruent

Answer

one pair of sides is parallel and one pair of angles is congruent

Answer

the diagonals are congruent

Answer

one pair of sides is congruent and one pair of angles is congruent

Question 47

The perimeter of rhombus TIGE is 68, and TG = 16.  The length of IE is

Accepted Answer

30

Answer

34

Answer

15

Answer

52

Question 48

In parallelogram PQRS, ST $\cong$SP and m∠R = 130°, what is m∠PST?

Accepted Answer

80

Answer

130

Answer

50

Answer

65

Question 49

Which information is NOT sufficient to prove that a parallelogram is a square?

Accepted Answer

The diagonals are perpendicular and one pair of adjacent sides are congruent.

Answer

The diagonals are both congruent and perpendicular.

Answer

The diagonals are perpendicular and one pair of adjacent sides are perpendicular.

Answer

The diagonals are congruent and one pair of adjacent sides are congruent.

Question 50

In parallelogram ABCD, diagonals AC and BD intersect at E.
Which statement proves ABCD is a rectangle?

Accepted Answer

AB ⊥ BD

Answer

AC $\cong$BD

Answer

AC⊥ BD

Answer

AC bisects ∠BCD

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