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Chapter 5: Q8 (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 XY is the median and ABandCDare the two bases of the trapezoid. Therefore, the length of the median is given by

XY=12AB+CD

03

Step 3. Description of step.

Substitute 3x+2 for AB, 2x+1for CD and 2x+4for XY into equation obtained in step 2 to find the value of x.

2x+4=123x+2+2x+12x+4=125x+34x+8=5x+3x=5

Therefore, the value of x is 5.

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Most popular questions from this chapter

Given:▱PQRS;localid="1637659881844" PJ¯≅RK¯

Prove: localid="1637659923835" SJ¯≅QK¯

Given: parallelogram ABCD; DE¯⊥AC¯; BF¯⊥AC¯.

Prove: DEBF is a parallelogram.

State the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

SA¯≅KC¯;SK¯≅AC¯

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

Given: m∠A=m∠C=x;m∠B=m∠D=y

Prove: ABCD is a parallelogram.

Proof:

The coordinates of the three vertices of a parallelogram are given. Find all the possibilities you can for the coordinates of the fourth vertex.

(3,4),(9,4),(6,8)
See all solutions

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