/*! 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} Q31 Given: ABCD is a 鈻�,聽CD炉鈮匔E... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q31 (page 170)

Given: ABCD is a 鈻�,CD炉鈮�CE炉

Prove: 鈭�A鈮�鈭�E

Short Answer

Expert verified

It is proved that 鈭�A鈮�鈭�E.

Step by step solution

01

Step 1. Apply properties of parallelogram.

Opposite angles of a parallelogram are congruent.

In 鈻�ABCD, 鈭�Aand 鈭�BCDare opposite angles. Therefore, 鈭�A鈮�鈭�BCD.

02

Step 2. Description of step.

From the given figure, it can be observed that BC炉鈭�AD炉and CD炉is a transversal then 鈭�BCDand 鈭�CDEare alternate interior angles such that, 鈭�BCD鈮�鈭�CDE.

03

Step 3. Isosceles triangle theorem.

If two sides of a triangle are congruent then the angles opposite to those sides are congruent.

Consider 螖CDE, in which CD炉鈮�CE炉then by isosceles triangle theorem, 鈭�CDE鈮�鈭�E

04

Step 4. Description of step.

As 鈭�A鈮�鈭�BCD, 鈭�BCD鈮�鈭�CDEand 鈭�CDE鈮�鈭�Ethen by the transitive property of congruence 鈭�A鈮�鈭�E.

Hence it is proved that 鈭�A鈮�鈭�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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

On a number line, point Ahas a coordinate -5and B has 3. Find the coordinate of the midpoint ofAB炉.

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

A trapezoid ___ has three congruent sides.

In Exercises 29-32, identify the level of measurement of the data as nominal, ordinal, interval, or ratio. Also, explain what is wrong with the given calculation.

Social Security Numbers As part of a project in a statistics class, students report the last four digits of their Social Security numbers, and the average (mean) of those digits is computed to be 4.7.

Draw the trapezoid described. If such a trapezoid cannot be drawn, explain why not.

With both bases shorter than the legs

Each diagram shows a trapezoid and its median. Find the value of x.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

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.