/*! 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} Q11. WE Write proofs in two鈥揷olumn for... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q11. WE (page 137)

Write proofs in two鈥揷olumn form.

Theorem 4鈥�1.

Short Answer

Expert verified

Statement

Reason

AB炉鈮�AC炉

Given

鈭�BAD鈮�鈭�CAD

Angle bisector theorem

AD炉鈮�AD炉

Reflexive property

螖BAD鈮�螖CAD

SAS postulate

鈭�B鈮�鈭�C

Congruent angles of congruent triangles

Step by step solution

01

Step 1. Draw an auxiliary line through angle A.

02

Step 2. Apply angle bisector theorem.

Angle bisector divides an angle into two equal parts.

From the figure in step 1 it can be observed thatAD炉 bisects 鈭�A.

Therefore, 鈭�BAD鈮�鈭�CAD.

03

Step 3. Reflexive property.

Reflexive property states that PQ炉鈮�PQ炉.

Therefore, AD炉鈮�AD炉.

04

Step 4. SAS postulate.

If two sides and included angle of one triangle are congruent to two sides and included angle of other triangle then the triangles are said to be congruent.

Here AB炉鈮�AC炉,AD炉鈮�AD炉 and 鈭�BAD鈮�鈭�CAD. Therefore,螖BAD鈮�螖CAD which implies that 鈭�B鈮�鈭�C.

It is proved that if the two sides of a triangle are congruent then the angles opposite to those sides are congruent.

05

Step 5. Two column proof.

Write a two-column proof based on above explanation.

Statement

Reason

AB炉鈮�AC炉

Given

鈭�BAD鈮�鈭�CAD

Angle bisector theorem

AD炉鈮�AD炉

Reflexive property

螖BAD鈮�螖CAD

SAS postulate

鈭�B鈮�鈭�C

Congruent angles of congruent triangles

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

For exercises 16-19 draw and label a diagram. List in terms of the diagram, what is given and what is to be proved. Then write a two column proof.

In two congruent triangles, if segments are drawn from two corresponding vertices perpendicular to the opposite sides, then those segments are congruent.

Explain how corollary 1 follows from theorem 4-1 such that an equilateral triangle is also equiangular.

For the following figure, state which congruence method can be used to prove the triangle congruent. If no method applies, say none.

Complete.

A method that can be used to prove right triangles congruent, but cannot be used with other types of triangles, is the?_method.

Decide whether you can deduce by the SSS, SAS, or ASA postulate that another triangle is congruent to 螖ABC. If so, write the congruence and name the postulate used. If not, write no congruence can be deduced.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Calculus

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.