Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Q. 20 (page 198)

MN¯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¯ 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+DI22−8=DI14=DI

Therefore the length D of is 14.

03

- Write the complete statement.

If ZO=8and MN=11, then DI=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!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Suppose you know that △SOK≅△COA. Explain how you could prove that quadrilateral SACK is a parallelogram.

The pliers shown are made in such a way that the jaws are always parallel. Explain.

M, N and T are the midpoints of the sides of ΔXYZ.

If TN=7, thenXY=?¯

Write a paragraph proof.

Given: ▱ABCD;  ▱BEDF

Prove: AECF is a ▱.

(Hint: A short proof is possible if certain auxiliary segments ate drawn.)

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.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free