Question 1

In the diagram, points D, O, and G are midpoints.  If AC = 10, AT = 18, and CT = 22, what is the perimeter of parallelogram CDOG ?

Accepted Answer

32

Answer

25

Answer

40

Answer

21

Question 2

In the diagram of isosceles trapezoid DEFG, DE || GF.  The value of x is

Accepted Answer

3

Question 3

In the diagram, the vertices of △DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of △ABC is 36 cm.  What is the length of DE?

Accepted Answer

6

Answer

4

Answer

12

Answer

18

Question 4

The diagram shows isosceles trapezoid ABCD with AB || DC and AD $\cong$BC. The m∠BAD is

Accepted Answer

70˚

Question 5

EF is the median of trapezoid ABCD.  If AB = 5x - 9, DC = x + 3, and EF = 2x + 2, what is the value of x?

Accepted Answer

5

Answer

2

Answer

8

Answer

7

Question 6

In the diagram, DE joins the midpoints of two sides of  ∆ABC.  Which statement is NOT true?

Accepted Answer

Area of ∆CDE = 1/2 area of ∆CAB

Answer

CE = 1/2 CB

Answer

Perimeter of ∆CDE = 1/2 perimeter of ∆CAB

Answer

DE = 1/2 AB

Question 7

In the diagram of ∆UVW, A, B, and C are midpoints.If VW = 7x - 3 and AB = 3x + 1, what is the length of VC?

Accepted Answer

16

Answer

32

Answer

5

Answer

13

Question 8

In the diagram of  ∆ABC, DE and DF are midsegments.  If DE = 9 and BC = 17, the perimeter of quadrilateral FDEC is

Accepted Answer

35

Question 9

Isosceles trapezoid ABCD has diagonals AC and BD. If AC = 5x + 13 and BD = 11x – 5, what is the value of x?

Accepted Answer

3

Answer

10

Answer

8

Answer

28

Question 10

In the diagram of trapezoid RSUT, RS || TU, X is the midpoint of RT, and V is the midpoint of SU.  If RS = 30 and XV = 44, what is the length of TU?

Accepted Answer

58

Answer

74

Answer

37

Answer

118

Question 11

In the diagram of △ABC, D is the midpoint of AB, and E is the midpoint of BC.  Which expression represents DE?

Accepted Answer

2x + 5

Answer

2x + 10

Answer

x + 2.5

Answer

8x + 20

Question 12

In the diagram of isosceles trapezoid ABCD, BC || AD and AB $\cong$CD.  If  CD = 25, AD = 26, and BC = 12, what is the length of an altitude of the trapezoid?

Accepted Answer

24

Answer

19

Answer

14

Answer

7

Question 13

In trapezoid ABCD, AB || CD and AD $\cong$BC.  What is the measure of angle D?

Accepted Answer

60

Answer

90

Answer

25

Answer

35

Question 14

In ∆ABC, midsegments MN, ML, and NL are drawn.  If MN = 8, ML = 5, and NL = 6, the perimeter of trapezoid BMNC is

Accepted Answer

35

Answer

26

Answer

31

Answer

28

Question 15

In trapezoid QRST, QR || ST and QT $\cong$RS.  If m∠Q = 5x + 3 and m∠R = 7x - 15, what is m∠Q?

Accepted Answer

48

Answer

16

Answer

83

Answer

9

Question 16

What is the perimeter of the triangle formed by connecting the midpoints of the sides of ∆ABC?

Accepted Answer

20

Question 17

In isosceles trapezoid ABCD, AD || BC and AB $\cong$CD. If BC = 20, AD = 36, and
AB = 17, what is the length of the altitude of the trapezoid?

Accepted Answer

15

Answer

10

Answer

16

Answer

12

Question 18

In the diagram of △ABC, DE is a midsegment of △ABC, DE = 7, AB = 10, and BC = 13.  The perimeter of △ABC is

Accepted Answer

37

Question 19

In the diagram, LATE is an isosceles trapezoid with LA || TE and LE $\cong$AT,  LA = 24, ET = 40, and AT = 10. The length of LF is

Accepted Answer

6

Answer

8

Answer

3

Answer

4

Question 20

In ∆ABC, D, E, and F are midpoints.  If AB = 20, BC = 12, and AC = 16, what is the perimeter of trapezoid ABEF?

Accepted Answer

44

Answer

40

Answer

36

Answer

24

Question 21

Trapezoid RSTV has RS || VT.  If trapezoid RSTV is not isosceles, which triangle is equal in area to ∆RSV?

Accepted Answer

∆SRT

Answer

∆RVT

Answer

∆STV

Answer

∆QRS

Question 22

In ∆ABC, D and E are midpoints.  If AC = 3x - 15 and DE = 6, what is the value of x?

Accepted Answer

9

Answer

7

Answer

6

Answer

12

Question 23

In the diagram, AB and CD are bases of trapezoid ABCD.  If m∠B  = 123 and m∠D = 75, what is m∠C?

Accepted Answer

57

Answer

75

Answer

105

Answer

123

Question 24

In the diagram, DE, DF, and EF are midsegments of  ∆ABC.
The perimeter of quadrilateral ADEF is equivalent to

Accepted Answer

AB + AC

Answer

1/2 (AB) + 1/2 (AC)

Answer

2•AB + 2•AC

Answer

AB + BC + AC

Question 25

In ∆ABC, D, E, and F are midpoints.  What is the ratio of the area of  ∆CFE to the area of  ∆CAB?

Accepted Answer

1:4

Answer

1:2

Answer

1:1

Answer

1:3

Question 26

In the diagram of equilateral triangle ABC, EF is a midsegment.  If EF = 2x + 8 and AB = 7x - 2, what is the perimeter of trapezoid ABFE?

Accepted Answer

100

Answer

60

Answer

120

Answer

36

Question 27

In trapezoid QRST, QR || ST and QT $\cong$RS.  ST = 32, QR = 56, and the perimeter of QRST is 144.  The length of QT is

Accepted Answer

28

Question 28

If m<ABE = 18˚, determine m<DAE.

Accepted Answer

72

Question 29

The m<EBC = 66˚.  What is m<DCE?

Accepted Answer

24

Question 30

In the kite, m<BAD = 140˚ and m<BCD = 30˚.  What is m<ABC?

Accepted Answer

95

Question 31

In the kite, m<ABC = 100˚ and m<BCE = 20˚.  What is m<BAD?

Accepted Answer

120˚

Question 32

In the kite, AC = 18 and BD = 12.  What is the length of BE?

Accepted Answer

6

Question 33

In kite ABCD, AB = 15 and the perimeter of ABCD is 100.  The length of CD is

Accepted Answer

35

Question 34

In kite ABCD, m<BAD = 106˚.  What is m<EAB?

Accepted Answer

53˚

Question 35

In kite ABCD, m<EDC = 70.  What is m<BCE?

Accepted Answer

20˚

Question 36

In kite ABCD, BE = 10.  What is BD?

Accepted Answer

20

Question 37

In kite ABCD, what is m<AEB?

Accepted Answer

90

Question 38

In kite ABCD, m<BAE = 65.  What is m<ADE?

Accepted Answer

25˚

Question 39

In kite ABCD, CD = 32 and AB = 15.  What is the perimeter of ABCD?

Accepted Answer

94

Question 40

In kite ABCD, m<BCD = 38˚.  What is m<CDE?

Accepted Answer

71

Question 41

in kite ABCD, m<ABC = 120 and m<CBE =  2•m<ABE.  What is m<ABE?

Accepted Answer

40

Question 42

In quadrilateral ABCD, AB || CD, and E, H, and F are the midpoints of AD, AC, and BC, respectively. If AB = 24, CD = 18, and AH = 10, then FH is

Accepted Answer

12

Answer

10

Answer

21

Answer

9

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