Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Q16 (page 169)

Given: ABCXis a is a localid="1637648903053" ▱,DXFEis a ▱.

Prove: ∠B≅∠E

Short Answer

Expert verified

It is proved that ∠B≅∠E.

Step by step solution

01

Step 1. Property of parallelogram.

The opposite angles of a parallelogram are congruent.

It is given that ABCX is a parallelogram in which ∠Band ∠AXCare opposite angles of a parallelogram. Then by property of parallelogram, ∠B≅∠AXC.

02

Step 2. Vertical opposite angles.

From the figure, it can be observed that ∠AXCand ∠DXFare vertically opposite angles. Therefore, by the definition of vertically opposite angles, ∠AXC≅∠DXF.

03

Step 3. Property of parallelogram.

It is given that DEFX is a parallelogram in which ∠Eand ∠DXFare opposite angles of a parallelogram. Then by property of parallelogram, ∠DXF≅∠E.

As ∠B≅∠AXC, ∠AXC≅∠DXFand ∠DXF≅∠E. It can be concluded that ∠B≅∠E.

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

State the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

∠SKC≅∠CAS;∠KCA≅∠ASK

Given: parallelogram ABCD; DE¯⊥AC¯; BF¯⊥AC¯.

Prove: DEBF is a parallelogram.

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

If XZ=10, then MN=?¯

State the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

SA¯≅KC¯;SA¯∥KC¯

Given: PlaneX∥PlaneY;LM¯≅ON¯

Prove: LMNO is a parallelogram.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

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