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Chapter 5: Q4 (page 192)

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

Short Answer

Expert verified

The value of x is 5.

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 FC is the median and AB and ED are the two bases of the trapezoid. Therefore, the length of the median is given by

FC=12AB+ED

03

Step 3. Description of step.

Substitute x for AB, 21 for ED, and 13 for FC into the equation obtained in step 2 to find the value of x.

13=12x+2126=x+21x=26鈭�21=5

Therefore, the value of x is 5.

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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.

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

Give the reason for each step in the following proof of theorem 5-6

Given: m鈭�A=m鈭�C=x;m鈭�B=m鈭�D=y

Prove: ABCD is a parallelogram.

Proof:

M, N and T are the midpoints of the sides of 螖XYZ.

State the theorem suggested by Exercise 6.

鈻�DECKis a parallelogram. Complete.

Ifm鈭�1=3x,m鈭�2=4x and m鈭�3=x2-70then x=?andm鈭�CED=? (numerical answers).
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