Chapter 5: Q20 (page 198)

$\bar{M N}$ is the median of trapezoid $Z O I D$ .
If localid="1638355391309" $Z O = 8$ and $M N = 11$ , then $D I = \underline{}$ .

Short Answer

Expert verified

If $Z O = 8$ and $M N = 11$ , then $D I = 14$ .

Step by step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. 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 that $\bar{M N}$ is the median of trapezoid $Z O I D$ .

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

Therefore, by using the theorem 5-19 it can be noticed that the median $\bar{M N}$ is parallel to the bases ZO and DI and has a length equal to the average of the base lengths ZO and DI.

Therefore, $M N = \frac{1}{2} (Z O + D I)$ .

Therefore, it can be obtained that:

$\begin{matrix} M N = \frac{1}{2} (Z O + D I) \\ 11 = \frac{1}{2} (8 + D I) \\ 22 = 8 + D I \\ 22 - 8 = D I \\ 14 = D I \end{matrix}$

Therefore the length of DI is 14.

Step 3. Write the complete statement.

If $Z O = 8$ and $M N = 11$ , then $D I = 14$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

$\bar{M N}$ is the median of trapezoid $Z O I D$ .
If localid="1638355391309" $Z O = 8$ and $M N = 11$ , then $D I = \underline{}$ .

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Description of step.

Step 3. Write the complete statement.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Decision Maths

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

MN¯is the median of trapezoid ZOID.If localid="1638355391309" ZO=8and MN=11, then DI=¯.

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Description of step.

Step 3. Write the complete statement.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Decision Maths

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

$\bar{M N}$ is the median of trapezoid $Z O I D$ .
If localid="1638355391309" $Z O = 8$ and $M N = 11$ , then $D I = \underline{}$ .