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Chapter 5: Q3 (page 180)

Points A, B, E and F are midpoints of XC炉,XD炉,YC炉and YD炉. Complete.

If AB=5x鈭�8, andEF=3x then x= ? .

Short Answer

Expert verified

x=4

Step by step solution

01

Step 1. Consider the diagram.

Here, A, B, E and F are the midpoints of sides XC炉,XD炉,YC炉and YD炉respectively.

And AB=5x鈭�8and EF=3x.

02

Step 2. Show the calculation.

Consider the triangle 鈻�XCD.

Here, points A and B are the midpoints of XC炉and XD炉.

So, by theorem 5-11 part (2), the side AB炉is half as long as the third side CD炉.

AB=12CD 鈥︹�� (1)

Consider the triangle 鈻�YCD.

Here, points E and F are the midpoints of YC炉and YD炉.

So, by theorem 5-11 part (2), the side EF炉is half as long as the third side CD炉.

EF=12CD 鈥︹�� (2)

From (1) and (2),

AB=EF

Substitute AB=5x鈭�8and EF=3x.

5x鈭�8=3x5x鈭�3x=82x=8x=4

03

Step 3. State the conclusion.

Therefore, x=4.

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Most popular questions from this chapter

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

AD炉鈭�BC炉

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

For the following figure, if OE=4and WE=8, name two segments congruent to WE炉.

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

AD炉鈮�BC炉

For exercises, 14-18 write paragraph proofs.

Given: ABCD is a parallelogram; DE=BF.

Prove: AFCE is a parallelogram.
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