Q20 MN炉聽is the median of trapezoid... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 5: Q20 (page 198)

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

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 $\overset{炉}{M N}$ 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 $\overset{炉}{M N}$ 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:

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

Therefore the length of DI is 14.

Step 3. Write the complete statement.

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

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91影视

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

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Description of step.

Step 3. Write the complete statement.

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91影视

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

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

Calculus

Pure Maths

Discrete Mathematics

Decision Maths

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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