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Chapter 5: Q13 (page 180)

AE鈫�,BF鈫�,CG鈫�and DH鈫�are parallel, with EF=FG=GH. Complete.

If AC=22鈭�x and BD=3x鈭�22 then x= ? .

Short Answer

Expert verified

The length of x is 11 units.

Step by step solution

01

Step 1. Consider the diagram.

The parallel lines are shown as:

AE, BF, CG and DH are parallel to each other and EF=FG=GH. Length of AC and BD are 22鈭�x and3x鈭�22 respectively.

02

Step 2. Show the calculation.

Here, ADHE is the trapezoid as AE is parallel to DH.

As EF=FG=GH and AE, BF, CG and DH are parallel to each other, then, the lines BF and CG are the midsegment of the trapezoid.

Hence,

AB=BC=CD

The length of AC is:

AC=AB+BC=BC+BC

Then,

AC=2BC 鈥︹�� (1)

The length of BD is:

BD=BC+CD=BC+BC

Then,

BD=2BC 鈥︹�� (2)

From equations (1) and (2), the length AC is equal to BD.

The length of x is calculated as follows:

AB=BD22鈭�x=3x鈭�224x=44x=11

Thus, the length of x is 11 units.

03

Step 3. State the conclusion.

Therefore, the length of x is 11 units.

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Most popular questions from this chapter

From the following figure P,Q,R,Sare the midpoints of the sides of quadrilateral ABCD. In this diagram PR炉and SQ炉 have the same midpoint O. If you think this will be the case for any quadrilateral ABCD, prove it. If not, tell what other information you need to know about quadrilateral ABCDbefore you can conclude that PR炉and SQ炉have the same midpoint.

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

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

Prove Theorem 5-1.

Given: PQ炉, RS炉and TU炉are each perpendicular to UQ鈫�;

R is the midpoint of PT炉;

Prove: R is equidistant from U and Q.
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