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Chapter 5: Q21 (page 175)

What values must x and y have to make the quadrilateral a parallelogram?

Short Answer

Expert verified

The values that x and y must have to make the quadrilateral a parallelogram are 10 and 2 respectively.

Step by step solution

01

Step 1. Observe the given diagram.

The given diagram is:

02

Step 2. Description of step.

In a parallelogram, both pairs of opposite sides are congruent.

Therefore, to make the given quadrilateral a parallelogram, the pairs of opposite sides are congruent.

Therefore, it can be obtained as:

4x+y=4213x鈭�2y=262

From the equation, it can be obtained as:

4x+y=42y=42鈭�4x

03

Step 3. Find the value of x.

Now, substitute the value of y in equation (2) to find the value of x.

Therefore, the value of x can be obtained as:

3x鈭�242鈭�4x=263x鈭�84+8x=2611x鈭�84=2611x=26+8411x=110x=11011x=10

Therefore, the value of x is 10.

04

Step 4. Find the value of y.

Now, substitute 10 for x in the equation y=42鈭�4xto find the value of y.

Therefore, the value of y can be obtained as:

y=42鈭�410=42鈭�40=2

Therefore, the value of y is 2.

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Most popular questions from this chapter

鈻�DECKis a parallelogram. Complete.

If m鈭�1=42,m鈭�2=x2and m鈭�CED=13xthen m鈭�2=?or m鈭�2=?(numerical answers).

The legs of this ironing board are built so that BO=AO=RO=DO.

What theorem guarantees that the board is parallel to the floor AR炉鈭�BD炉?

Draw a quadrilateral that is not a parallelogram but that has one pair of congruent sides and one pair of parallel sides.

You can use a sheet of lined notebook paper to divide a segment into a number of congruent parts. Here a piece of cardboard with edge AB炉is placed so that AB炉is separated into five congruent parts. Explain why it works.

Parallel rulers, used to draw parallel lines, are constructed so that EF=HGand HE=GF. Since there are hinges at points E, F, G and H, you can vary the distance between role="math" localid="1637730770232" HG鈫�and role="math" localid="1637730792914" EF鈫�. Explain why HG鈫�and EF鈫�are always parallel.
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