AnswersFall 24 GMS Geometry Concepts and Connections BLaw of Sines (Sec 8-3)

Proving a Quadrilateral Is a Parallelogram Answers

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1
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Figure ABCD is a parallelogram.

Question illustration
A
3
B
5
C
17
D
25
2
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Figure LMNO is a parallelogram.

Question illustration
A
8
B
10
C
13
D
20
3

Figure JKLM is a parallelogram. The measures of line segments MT and TK are shown.

Question illustration
A
1
B
2
C
7
D
8
4

Figure ABCD is a parallelogram.

Question illustration
A
First prove ABC is congruent to CDA, and then state AD and BC are corresponding sides of the triangles.
Option A
B
First prove ABC is similar to CDA, and then state AD and BC are opposite sides of the parallelograms.
Option B
C
First prove ABCD is congruent to CDAB, and then state AD and BC are corresponding sides of two parallelograms.
Option C
D
First prove ABCD is similar to CDAB, and then state AD and BC are opposite sides of the parallelograms.
Option D
5

Figure TUVS is a parallelogram.

Question illustration
A
angles T and V
B
angles S and U
C
angles U and V
D
angles S and T
6

Figure ABCD is a parallelogram.

Question illustration
A
∠B = 55°; ∠D = 55°
B
∠B = 55°; ∠D = 125°
C
∠B = 97°; ∠D = 97°
D
∠B = 83°; ∠D = 97°
7

Lourdes is making a frame in the shape of a parallelogram. She adds diagonal braces to strengthen the frame.

Question illustration
A
8 cm
B
16 cm
C
30 cm
D
60 cm
8

A vegetable garden is in the shape of a parallelogram with the dimensions shown.

Question illustration
A
54 feet
B
68 feet
C
108 feet
D
140 feet
9

Figure ABCD is a parallelogram.

Question illustration
A
AB = 4; BC = 16
B
AB = 4; BC = 8
C
AB = 10; BC = 20
D
AB = 10; BC = 28
10

Yolanda is making a banner for a school pep rally. She cuts fabric in the shape of a parallelogram. The angle at the bottom-left corner measures 80°.

Question illustration
A
40
B
50
C
100
D
160
11

Figure ABCD is a parallelogram.

Question illustration
A
∠B = 55°; ∠D = 55°
B
∠B = 55°; ∠D = 125°
C
∠B = 97°; ∠D = 97°
D
∠B = 83°; ∠D = 97°
12

Figure TUVS is a parallelogram.

Question illustration
A
angles T and V
B
angles S and U
C
angles U and V
D
angles S and T
13

Lourdes is making a frame in the shape of a parallelogram. She adds diagonal braces to strengthen the frame.

Question illustration
A
8 cm
B
16 cm
C
30 cm
D
60 cm
14

Figure ABCD is a parallelogram.

Question illustration
A
14 units
B
38 units
C
44 units
D
49 units
15

Figure ABCD is a parallelogram.

Question illustration
A
6
B
7
C
8
D
9
16

The parallelogram shown represents a map of the boundaries of a natural preserve. Walking trails run from points A to C and from points B to D. The measurements shown represent miles.

Question illustration
A
6 miles
B
12 miles
C
16 miles
D
36 miles
17

Figure ABCD is a parallelogram.

Question illustration
A
3
B
5
C
17
D
25
18

Yolanda is making a banner for a school pep rally. She cuts fabric in the shape of a parallelogram. The angle at the bottom-left corner measures 80°.

Question illustration
A
40
B
50
C
100
D
160
19

Figure ABCD is a parallelogram.

Question illustration
A
AB = 4; BC = 16
B
AB = 4; BC = 8
C
AB = 10; BC = 20
D
AB = 10; BC = 28
20

Which equations are correct? Select three options.

A
n = 10
B
n = 7
C
CF = 59
D
FE = 42
E
CD = 30

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