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Chapter 5: Q20 (page 170)

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

Short Answer

Expert verified

The value of x and y is 7 and 18 respectively.

Step by step solution

01

Step 1. Apply property of parallelogram.

Diagonals of a parallelogram bisect each other, that is, two segments of each diagonal are equal to one another.

In a given figure, by the property of a parallelogram,

3x+4=25;2y鈭�8=28

02

Step 2. Description of step.

Subtract 4 from both sides of 3x+4=25.

3x+4鈭�4=25鈭�43x=21

03

Step 3. Description of step.

Divide each side of 3x=21 by 3 to obtain the value of x.

3x3=213x=7

04

Step 4. Description of step.

Add 8 on both sides of 2y鈭�8=28.

2y鈭�8+8=28+82y=36

05

Step 5. Description of step.

Divide each side of 2y=36 by 2 to obtain the value of y.

2y2=362y=18

Therefore, the value of x and y is 7 and 18 respectively.

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Most popular questions from this chapter

For exercises, 14-18 write paragraph proofs.

Given: parallelogram ABCD, AN炉bisects 鈭�DAB; CM炉bisects 鈭�BCD.

Prove: AMCN is a parallelogram.

Draw and label a diagram. List what is given and what is to be proved. Then write a two-column proof of the theorem.

Theorem 5-7.

State the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

SA炉鈭�KC炉;role="math" localid="1637731683825" SK炉鈭�AC炉

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

State the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

鈭�SKC鈮�鈭�CAS;鈭�KCA鈮�鈭�ASK
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