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Chapter 5: Q. 20 (page 198)

MN炉is the median of trapezoid ZOID.

20. IfZO=8 andMN=11 , then DI=?_.

Short Answer

Expert verified

IfZO=8 andMN=11 , thenDI=14 .

Step by step solution

01

­- Observe the given diagram.

The given diagram is:

02

- Description of step.

The theorem 5-19 states that the median of a trapezoid is parallel to the bases and has a length equal to the average of the base lengths.

It is being given thatMN炉 is the median of trapezoid ZOID.

From the given diagram it can be noticed the sidesZOandDI are parallel sides, therefore the bases of the trapezoid are and .

Therefore, by using the theorem 5-19 it can be noticed that the median is parallel to the basesand and has a length equal to the average of the base lengths and .

Therefore,MN=12(ZO+DI).

Therefore, it can be obtained that:

MN=12(ZO+DI)11=12(8+DI)22=8+DI22鈭�8=DI14=DI

Therefore the length D of is 14.

03

- Write the complete statement.

If ZO=8and MN=11, then DI=14.

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