Question

hausen - sem 2 / module 6: quadrilaterals / january 12th-16th

1. find the missing side length of the parallelogram:

image of three parallelograms with some side lengths labeled
a. 23.5
b. 21.7
c. 15
d. 15.7
e. 10.85
f. 7.85

Explanation:

To solve for the missing side lengths of the parallelograms, we use the property of parallelograms: opposite sides of a parallelogram are equal in length.

1. Parallelogram \( WXYZ \) (or \( WVUX \))

• Given side \( WV = 15.7 \).
• In a parallelogram, opposite sides are equal, so \( XU = WV \).
• Thus, the missing side \( XU = 15.7 \).

2. Parallelogram \( GFEH \) (or \( GFHE \))

• Given side \( GF = 21.7 \).
• In a parallelogram, opposite sides are equal, so \( HE = GF \).
• Thus, the missing side \( HE = 21.7 \).

3. Parallelogram \( QRSP \) (or \( QRPS \))

• Given side \( QR = 23.5 \).
• In a parallelogram, opposite sides are equal, so \( PS = QR \).
• Thus, the missing side \( PS = 23.5 \).

Final Answers (matching the options):

1. For the first parallelogram, the missing side is \( \boldsymbol{15.7} \) (option d).
2. For the second parallelogram, the missing side is \( \boldsymbol{21.7} \) (option b).
3. For the third parallelogram, the missing side is \( \boldsymbol{23.5} \) (option a).

(Note: The labels in the diagram may vary slightly, but the key property of opposite sides in a parallelogram being equal is consistent.)

Answer:

To solve for the missing side lengths of the parallelograms, we use the property of parallelograms: opposite sides of a parallelogram are equal in length.

1. Parallelogram \( WXYZ \) (or \( WVUX \))

• Given side \( WV = 15.7 \).
• In a parallelogram, opposite sides are equal, so \( XU = WV \).
• Thus, the missing side \( XU = 15.7 \).

2. Parallelogram \( GFEH \) (or \( GFHE \))

• Given side \( GF = 21.7 \).
• In a parallelogram, opposite sides are equal, so \( HE = GF \).
• Thus, the missing side \( HE = 21.7 \).

3. Parallelogram \( QRSP \) (or \( QRPS \))

• Given side \( QR = 23.5 \).
• In a parallelogram, opposite sides are equal, so \( PS = QR \).
• Thus, the missing side \( PS = 23.5 \).

Final Answers (matching the options):

1. For the first parallelogram, the missing side is \( \boldsymbol{15.7} \) (option d).
2. For the second parallelogram, the missing side is \( \boldsymbol{21.7} \) (option b).
3. For the third parallelogram, the missing side is \( \boldsymbol{23.5} \) (option a).

(Note: The labels in the diagram may vary slightly, but the key property of opposite sides in a parallelogram being equal is consistent.)