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Chapter 5: Q1 (page 192)

Each diagram shows a trapezoid and its median. Find the value of x.

Short Answer

Expert verified

The value of x is 12.

Step by step solution

01

Step 1. Label the diagram.

02

Step 2. Apply the property of trapezoid.

The length of the median of the trapezoid is equal to the average length of the two bases.

From the given figure it can be observed that XY is the median and AB and DC are the two bases of the trapezoid. Therefore, the length of the median is given by

XY=12AB+DC

03

Step 3. Description of step.

Substitute 9 for AB, 15 for DC, and x for XY into the equation obtained in step 2 to find the value of x.

x=129+15=12脳24=12

Therefore, the value of x is 12.

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Most popular questions from this chapter

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.

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.

For exercises, 14-18 write paragraph proofs.

Given: parallelogram ABCD, M and N are the midpoints of AB炉and DC炉.

Prove: AMCN is a parallelogram.

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

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.
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