/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q23. Draw any ∠AOB and its bisecto... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Log out

Learning Materials

Features

Discover

Chapter 2: Q23. (page 64)

Draw any∠AOB and its bisector role="math" localid="1646847955601" OE↔. Now draw the rays opposite to OA↔,OB↔ and OE↔. What can you conclude about the part of the diagram shown in red? Prove your conclusion.

Short Answer

Expert verified

The thing that can be concluded about the part of the diagram shown in red is that the ray OF→bisects the angle ∠CODthat implies role="math" localid="1646848105169" ∠3≅∠4.

The proof of the conclusion is:

It is being given that OE→is the bisector of ∠AOB.

Therefore, ∠1≅∠2.

From the diagram, it can be noticed thatangles∠1 and∠4are the vertically opposite angles.

Therefore, ∠1≅∠4.

From the diagram, it can be noticed that angles∠2 and∠3 are the verticallyopposite angles.

Therefore, ∠2≅∠3.

Now, it can be noticed that:

∠1=∠2∠4=∠2∵∠1≅∠4∠4=∠3∵∠2≅∠3

Therefore, ∠3≅∠4.

Therefore, it can be said that the ray OF→bisects the angle ∠COD.

Hence proved.

Step by step solution

01

Step 1. Observe the diagram.

The given diagram is:

02

Step 2. Description of step.

The thing that can be conclude about the part of the diagram shown in red is that the rayOF→ bisects the angle∠COD that implies ∠3≅∠4.

03

Step 3. Description of step.

It is being given thatOE→ is the bisector of ∠AOB.

Therefore, ∠1≅∠2.

From the diagram it can be noticed that theangles∠1 and∠4 are the vertically opposite angles.

Therefore, ∠1≅∠4.

From the diagram it can be noticed that the angles∠2 and∠3 are the verticallyopposite angles.

Therefore, ∠2≅∠3.

Now, it can be noticed that:

∠1=∠2∠4=∠2∵∠1≅∠4∠4=∠3∵∠2≅∠3

Therefore, ∠3≅∠4.

Therefore, it can be said thatthe rayOF→ bisects the angle ∠COD.

Hence proved.

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.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

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

Write each biconditional as two conditionals that are converses of each other.

Points lie in one plane if and only if they are coplanar.

State the number that is paired with the bisector of ∠CDE.

State the hypothesis and the conclusion of each conditional.

I can’t sleep if I’m not tired.

Justify each step.

3a2=653a=125a=45

State which postulate, definition, or theorem justifies the statement about the diagram.

If ∠BEC≅∠CEF, thenEC→ is the bisector of ∠BEF .
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

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.