Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q13. CT (page 113)

Given: AB¯∥CD¯; BF¯bisects ∠ABE; DG¯bisects ∠CDB.

Prove: BF¯∥DG¯

Short Answer

Expert verified

It is proved that BF¯∥DG¯.

Step by step solution

01

Step 1. Draw a diagram.

02

Step 2. Description of step.

As per the given information,BF¯bisects∠ABEandDG¯bisects∠CDBwhich implies that,

∠ABF=∠FBE∠CDG=∠GDB

03

Step 3. Description of step.

If two parallel lines are bisected by a transversal then the corresponding angles are congruent.

Here,AB¯∥CD¯andDE¯is transversal then ∠CDX≅∠ABD.

04

Step 4. Description of step.

Now, ∠CDX+∠CDG+∠GDB=180and ∠ABD+∠ABF+∠FBE=180then from these two equations we get,

∠CDX+∠CDG+∠GDB=∠ABD+∠ABF+∠FBE∠CDX+∠CDG+∠CDG=∠ABD+∠ABF+∠ABF∠CDX+2∠CDG=∠ABD+2∠ABF2∠CDG=2∠ABF∠CDG=∠ABF

05

Step 5. Description of step.

If two parallel lines are bisected by a transversal then the corresponding angles are congruent.

Here,AB¯∥CD¯andGD¯is transversal then ∠CDG≅∠AYG.

06

Step 6. Description of step.

As∠CDG≅∠ABFand∠CDG≅∠AYGimplies ∠ABF≅∠AYG, which are corresponding angles. Therefore, BF¯∥DG¯.

Hence it is proved that BF¯∥DG¯.

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

Classify each pair of angles as alternate interior angles, same-side interior angles, corresponding angles, or none of these.

and

Complete each statement with the word always, sometimes, or never.

Three lines intersecting in one point are coplanar

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.

and

Complete each statement with the word always, sometimes, or never.

Two planes parallel to the same line are parallel to each other

Assume that a∥band c∥d, name all angels congruent to ∠2.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

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