AnswersRMA FL-1206310-Geometry Semester 2Proving a Quadrilateral Is a Parallelogram

Proving a Quadrilateral Is a Parallelogram Answers

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1
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Parallelogram L O N M is shown. Diagonals are drawn from point L to point N and from point O to point M and intersect at point Q. The length of line segment O Q is (2 x + 3) centimeters and the length of lines segment Q M is (3 x minus 4) centimeters.

Question illustration
A
7 cm
B
17 cm
C
24 cm
D
34 cm
2
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Parallelogram W X Y Z is shown. The length of W X is (2 x + 9) millimeters and the length of W X is (x minus 5) millimeters.

Question illustration
A
2 mm
B
7 mm
C
23 mm
D
25 mm
3

Parallelogram L M N O is shown. Angle L is (2 x + 10) degrees and angle O is (x + 20) degrees.

Question illustration
A
50°
B
70°
C
110°
D
130°
4

Given: AD ≅ BC and AD ∥ BCProve: ABCD is a parallelogram. Statements Reasons 1. AD ≅ BC; AD ∥ BC 1. given 2. ∠CAD and ∠ACB are alternate interior ∠s 2. definition of alternate interior angles 3. ∠CAD ≅ ∠ACB 3. alternate interior angles are congruent 4. AC ≅ AC 4. reflexive property 5. △CAD ≅ △ACB 5. SAS congruency theorem 6. AB ≅ CD 6. ? 7. ABCD is a parallelogram 7. parallelogram side theorem What is the missing reason in step 6?

Question illustration
A
SSS congruency theorem
B
CPCTC
C
definition of a parallelogram
D
opposite sides in a parallelogram are congruent
5

Parallelogram L M N O is shown. Angle N is (2 x) degrees and angle L is (3 x minus 20) degrees.

Question illustration
A
20°
B
30°
C
40°
D
50°
6

Parallelogram R S T U is shown. Diagonals are drawn from point R to point T and from point U to point S and intersect at point V. The length of line segment U V is (x minus 3) meters and the length of line segment V S is (3 x minus 13) meters.

Question illustration
A
2
B
4
C
5
D
10
7

Parallelogram L M N O is shown. Angle M is (3 x minus 55) degrees, angle N is (5 y) degrees, and angle O is (2 x) degrees.

Question illustration
A
x = 11, y = 14
B
x = 11, y = 25
C
x = 55, y = 14
D
x = 55, y = 25
8

Parallelogram P Q S R is shown. The length of P Q is (2 x + 5) centimeters and the length of R S is (4 x + 1) centimeters.

Question illustration
A
2 cm
B
5 cm
C
6 cm
D
9 cm
10

Parallelogram P Q S R is shown. The length of P Q is (4 x minus 1) centimeters and the length of R S is (3 x + 7) centimeters.

Question illustration
A
4 cm
B
6 cm
C
8 cm
D
12 cm
11

Parallelogram L M N O is shown. Angle L is (x + 40) degrees and angle O is (3 x) degrees.

Question illustration
A
35°
B
75°
C
105°
D
155
Option D
12

Parallelogram A B C D is shown. The length of A B is (9 x minus 14) inches and the length of D C is (3 x + 4) inches.

Question illustration
A
3 in.
B
9 in.
C
13 in.
D
19 in.
Option D
13

Parallelogram A B C D is shown. The length of A B is (8 x minus 5) inches and the length of D C is (3 x + 10) inches.

Question illustration
A
3 in.
B
4 in.
C
8 in.
D
19 in.
14

Parallelogram R S T U is shown. Diagonals are drawn from point R to point T and from point U to point S and intersect at point V. The length of line segment U V is (x + 3) meters and the length of line segment V S is (2 x minus 7) meters.

Question illustration
A
10 m
B
13 m
C
23 m
D
26 m
15

Parallelogram L M N O is shown. Angle N is (2 x) degrees and angle L is (3 x minus 20) degrees.

Question illustration
A
20°
B
30°
C
40°
D
50°
16

Parallelogram L M N O is shown. Angle L is (x + 40) degrees and angle O is (3 x) degrees.

Question illustration
A
35°
B
75°
C
105°
D
155
Option D
17

Parallelogram P Q S R is shown. The length of P Q is (4 x minus 1) centimeters and the length of R S is (3 x + 7) centimeters.

Question illustration
A
4 cm
B
6 cm
C
8 cm
D
12 cm
18

Parallelogram R S T U is shown. Diagonals are drawn from point R to point T and from point U to point S and intersect at point V. The length of line segment U V is (x + 3) meters and the length of line segment V S is (2 x minus 7) meters.

Question illustration
A
10 m
B
13 m
C
23 m
D
26 m
19

Quadrilateral W X Y Z is shown. Diagonals are drawn from point W to point Y and from point Z to point X and intersect at point C. The lengths of W C and C Y are congruent.

Question illustration
A
WXYZ is a parallelogram because diagonal XZ is bisected.
B
WXYZ is not necessarily a parallelogram because it is unknown if CZ = CY.
C
WXYZ is a parallelogram because ZC + CX = ZX.
D
WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
20

Given: AB ≅ CD and AD ≅ BCProve: ABCD is a parallelogram. Statements Reasons1.AB ≅ CD;AD ≅ BC1.given2.AC ≅ AC2.reflexive property3.△ADC ≅ △CBA3.?4.∠DAC ≅ ∠BCA; ∠ACD ≅ ∠CAB4.CPCTC5.∠DAC and ∠BCA are alt. int. ∠s;∠ACD and ∠CAB are alt. int. ∠s5.definition of alternate interior angles6.AB ∥ CD; AD ∥ BC6.converse of the alternate interior angles theorem7.ABCD is a parallelogram7.definition of parallelogramWhat is the missing reason in step 3?

Question illustration
A
triangle angle sum theorem
B
SAS congruency theorem
C
SSS congruency theorem
D
CPCTC
21

Parallelogram P Q S R is shown. The length of P Q is (2 x + 5) centimeters and the length of R S is (4 x + 1) centimeters.

Question illustration
A
2 cm
B
5 cm
C
6 cm
D
9 cm

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