Chapter 5: Q7 (page 182)

Given that $▱ A B C D$ and M is the midpoint of $\bar{A B}$ . Then prove that $M O = \frac{1}{2} A D$ .

Short Answer

Expert verified

The statement is $M O = \frac{1}{2} A D$ .

Step by step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Step description.

Consider that the two triangles $Δ M O B, Δ A D B$ .

Here $∠ B$ is common in both the angles such that $∠ M B O = ∠ A B D$ .

Since M is the midpoint of AB such that $\frac{M B}{A B} = \frac{1}{2}$ .

From the figure, the diagonals of the parallelogram intersect each other as $\frac{O B}{D B} = \frac{1}{2}$ .

Step 3. Step description.

By the SAS postulates, it is clear that $Δ M O B ~ Δ A D B$ .

Since $\frac{M O}{A D} = \frac{1}{2}$ thus $M O = \frac{1}{2} A D$

Therefore, $M O = \frac{1}{2} A D$ .

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.

Given that $▱ A B C D$ and M is the midpoint of $\bar{A B}$ . Then prove that $M O = \frac{1}{2} A D$ .

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Step description.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Mechanics Maths

Statistics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Given that ▱ABCD and M is the midpoint of AB¯. Then prove that MO=12AD.

Short Answer

Step by step solution

Step 1. Check the figure.

Step 2. Step description.

Step 3. Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Mechanics Maths

Statistics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Given that $▱ A B C D$ and M is the midpoint of $\bar{A B}$ . Then prove that $M O = \frac{1}{2} A D$ .