/*! 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} Q1. Use the condition: Two angles ar... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q1. (page 68)

Use the condition: Two angles are congruent if they are vertical angles.

a. Write the hypothesis.

b. Write the converse.

Short Answer

Expert verified

a. Two angles are vertical angles, then they are congruent.

b. The converse statement 鈥淚f two angles are congruent, they are vertical angles鈥� is false.

Step by step solution

01

Part a. Step 1. State the definition of vertical angle.

When two lines intersect to make an X, angles on opposite sides of the X are called vertical angles. These angles are equal and here is the official theorem that tells so.

02

Part a. Step 2. Sketch the diagram.

03

Part a. Step 3. State the conclusion.

Vertical angles are congruent:

If two angles are vertical angles, then they are congruent (from the figure above).

Vertical angles are one of the most frequently used things in proofs and other types of geometry problems, and they are one of the easiest things to spot in a diagram.

04

Part b. Step 1. State the converse of the statement.

If two angles are congruent, they are vertical angles.

05

Part b. Step 2. State the explanation.

Two angles of an isosceles triangle have the same measure (are congruent) but they are not vertical angles. So, if two angles are congruent that does not mean that they are vertical angles.

06

Part b. Step 3. State the conclusion.

Therefore, the converse is false.

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

Provide a counterexample to show that each statement is false.

Statement: If a four-sided figure has four congruent sides, then it has four right angles.

Tell whether each statement is true or false. Then write converse and tell whether it is true or false.

Statement: If m鈭�T=40then 鈭�Tis not obtuse.

Provide a counterexample to show that each statement is false.

Statement: If xy>5y, than x>5.

What can you conclude if the following sentences are all true?

  1. If(1) p, then q.
  2. (2) p
  3. I(3) q, then not r.

(4) s or r

Justify each step.

z+73=鈭�11

z+7=鈭�33

z=鈭�40
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Discrete 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.