McDougal Littell Jurgensen Geometry: Student Edition Geometry
McDougal Littell Jurgensen Geometry: Student Edition Geometry
5th Edition
ISBN: 9780395977279
Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Publisher: Houghton Mifflin Company College Division
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Chapter 4.5, Problem 17WE
To determine

To draw: and label a diagram, and to prove the given statement.

Expert Solution & Answer
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Explanation of Solution

Given information:

Given statement:

Segments are drawn from the endpoints of the base of an isosceles triangle perpendicular to the opposite legs, and then those segments are congruent.

Calculation:

Suppose if segments are drawn from the endpoints of the base of an isosceles triangle perpendicular to the opposite legs, then prove those segment are congruent.

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 4.5, Problem 17WE

The provided data is as follows:

Here, ΔXYZ is isosceles with XY¯XZ¯

Also, it is provided that

  ZA¯XY¯YB¯XZ¯

To prove: ZA¯YB¯

Show that ΔXBYΔXAZ

Consider these two triangles and follow the following steps provided in the table below:

    StatementsReasons
      1. ZA¯XY¯;YB¯XZ¯Given
      2. mXBY=90°;mXAZ=90°Definition of perpendicular line
      3. XBYXAZDefinition of congruent angle
      4. XXBy reflexive property
      5. XY¯XZ¯Provided
      6. ΔXBYΔXAZAAS theorem
      7. ZA¯YB¯CPCT

Therefore, the triangles ΔXBY and ΔXAZ are congruent by AAS property.

This implies that by congruent parts of congruent triangles CPCT are equal, that is ZA¯YB¯ .

Chapter 4 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

Ch. 4.1 - Prob. 11CECh. 4.1 - Prob. 12CECh. 4.1 - Prob. 13CECh. 4.1 - Prob. 14CECh. 4.1 - Prob. 15CECh. 4.1 - Prob. 16CECh. 4.1 - Prob. 17CECh. 4.1 - Prob. 18CECh. 4.1 - Prob. 19CECh. 4.1 - Prob. 20CECh. 4.1 - Prob. 1WECh. 4.1 - Prob. 2WECh. 4.1 - Prob. 3WECh. 4.1 - Prob. 4WECh. 4.1 - Prob. 5WECh. 4.1 - Prob. 6WECh. 4.1 - Prob. 7WECh. 4.1 - Prob. 8WECh. 4.1 - Prob. 9WECh. 4.1 - Prob. 10WECh. 4.1 - Prob. 11WECh. 4.1 - Prob. 12WECh. 4.1 - Prob. 13WECh. 4.1 - Prob. 14WECh. 4.1 - Prob. 15WECh. 4.1 - Prob. 16WECh. 4.1 - Prob. 17WECh. 4.1 - Prob. 18WECh. 4.1 - Prob. 19WECh. 4.1 - Prob. 20WECh. 4.1 - Prob. 21WECh. 4.1 - Prob. 22WECh. 4.1 - Prob. 23WECh. 4.1 - Prob. 24WECh. 4.1 - Prob. 1MRECh. 4.1 - Prob. 2MRECh. 4.2 - Prob. 1CECh. 4.2 - Prob. 2CECh. 4.2 - Prob. 3CECh. 4.2 - Prob. 4CECh. 4.2 - Prob. 5CECh. 4.2 - Prob. 6CECh. 4.2 - Prob. 7CECh. 4.2 - Prob. 8CECh. 4.2 - Prob. 9CECh. 4.2 - Prob. 10CECh. 4.2 - Prob. 11CECh. 4.2 - Prob. 1WECh. 4.2 - Prob. 2WECh. 4.2 - Prob. 3WECh. 4.2 - Prob. 4WECh. 4.2 - Prob. 5WECh. 4.2 - Prob. 6WECh. 4.2 - Prob. 7WECh. 4.2 - Prob. 8WECh. 4.2 - Prob. 9WECh. 4.2 - Prob. 10WECh. 4.2 - Prob. 11WECh. 4.2 - Prob. 12WECh. 4.2 - Prob. 13WECh. 4.2 - Prob. 14WECh. 4.2 - Prob. 15WECh. 4.2 - Prob. 16WECh. 4.2 - Prob. 17WECh. 4.2 - Prob. 18WECh. 4.2 - Prob. 19WECh. 4.2 - Prob. 20WECh. 4.2 - Prob. 21WECh. 4.2 - Prob. 22WECh. 4.2 - Prob. 23WECh. 4.2 - Prob. 24WECh. 4.2 - Prob. 25WECh. 4.2 - Prob. 26WECh. 4.2 - Prob. 27WECh. 4.3 - Prob. 1CECh. 4.3 - Prob. 2CECh. 4.3 - Prob. 3CECh. 4.3 - Prob. 4CECh. 4.3 - Prob. 5CECh. 4.3 - Prob. 6CECh. 4.3 - Prob. 1WECh. 4.3 - Prob. 2WECh. 4.3 - Prob. 3WECh. 4.3 - Prob. 4WECh. 4.3 - Prob. 5WECh. 4.3 - Prob. 6WECh. 4.3 - Prob. 7WECh. 4.3 - Prob. 8WECh. 4.3 - Prob. 9WECh. 4.3 - Prob. 10WECh. 4.3 - Prob. 11WECh. 4.3 - Prob. 12WECh. 4.3 - Prob. 13WECh. 4.3 - Prob. 14WECh. 4.3 - Prob. 15WECh. 4.3 - Prob. 16WECh. 4.3 - Prob. 1ST1Ch. 4.3 - Prob. 2ST1Ch. 4.3 - Prob. 3ST1Ch. 4.3 - Prob. 4ST1Ch. 4.3 - Prob. 5ST1Ch. 4.3 - Prob. 6ST1Ch. 4.3 - Prob. 7ST1Ch. 4.3 - Prob. 8ST1Ch. 4.4 - Prob. 1CECh. 4.4 - Prob. 2CECh. 4.4 - Prob. 3CECh. 4.4 - Prob. 4CECh. 4.4 - Prob. 5CECh. 4.4 - Prob. 6CECh. 4.4 - Prob. 7CECh. 4.4 - Prob. 8CECh. 4.4 - Prob. 9CECh. 4.4 - Prob. 10CECh. 4.4 - Prob. 11CECh. 4.4 - Prob. 12CECh. 4.4 - Prob. 1WECh. 4.4 - Prob. 2WECh. 4.4 - Prob. 3WECh. 4.4 - Prob. 4WECh. 4.4 - Prob. 5WECh. 4.4 - Prob. 6WECh. 4.4 - Prob. 7WECh. 4.4 - Prob. 8WECh. 4.4 - Prob. 9WECh. 4.4 - Prob. 10WECh. 4.4 - Prob. 11WECh. 4.4 - Prob. 12WECh. 4.4 - Prob. 13WECh. 4.4 - Prob. 14WECh. 4.4 - Prob. 15WECh. 4.4 - Prob. 16WECh. 4.4 - Prob. 17WECh. 4.4 - Prob. 18WECh. 4.4 - Prob. 19WECh. 4.4 - Prob. 20WECh. 4.4 - Prob. 21WECh. 4.4 - Prob. 22WECh. 4.4 - Prob. 23WECh. 4.4 - Prob. 24WECh. 4.4 - Prob. 25WECh. 4.4 - Prob. 26WECh. 4.4 - Prob. 27WECh. 4.4 - Prob. 28WECh. 4.4 - Prob. 29WECh. 4.4 - Prob. 30WECh. 4.4 - Prob. 31WECh. 4.4 - Prob. 32WECh. 4.4 - Prob. 33WECh. 4.4 - Prob. 34WECh. 4.5 - Prob. 1CECh. 4.5 - Prob. 2CECh. 4.5 - Prob. 3CECh. 4.5 - Prob. 4CECh. 4.5 - Prob. 5CECh. 4.5 - Prob. 6CECh. 4.5 - Prob. 7CECh. 4.5 - Prob. 8CECh. 4.5 - Prob. 9CECh. 4.5 - Prob. 10CECh. 4.5 - Prob. 11CECh. 4.5 - Prob. 12CECh. 4.5 - Prob. 13CECh. 4.5 - Prob. 14CECh. 4.5 - Prob. 1WECh. 4.5 - Prob. 2WECh. 4.5 - Prob. 3WECh. 4.5 - Prob. 4WECh. 4.5 - Prob. 5WECh. 4.5 - Prob. 6WECh. 4.5 - Prob. 7WECh. 4.5 - Prob. 8WECh. 4.5 - Prob. 9WECh. 4.5 - Prob. 10WECh. 4.5 - Prob. 11WECh. 4.5 - Prob. 12WECh. 4.5 - Prob. 13WECh. 4.5 - Prob. 14WECh. 4.5 - Prob. 15WECh. 4.5 - Prob. 16WECh. 4.5 - Prob. 17WECh. 4.5 - Prob. 18WECh. 4.5 - Prob. 19WECh. 4.5 - Prob. 20WECh. 4.5 - Prob. 21WECh. 4.5 - Prob. 22WECh. 4.5 - Prob. 1ST2Ch. 4.5 - Prob. 2ST2Ch. 4.5 - Prob. 3ST2Ch. 4.5 - Prob. 4ST2Ch. 4.5 - Prob. 5ST2Ch. 4.6 - Prob. 1CECh. 4.6 - Prob. 2CECh. 4.6 - Prob. 3CECh. 4.6 - Prob. 4CECh. 4.6 - Prob. 1WECh. 4.6 - Prob. 2WECh. 4.6 - Prob. 3WECh. 4.6 - Prob. 4WECh. 4.6 - Prob. 5WECh. 4.6 - Prob. 6WECh. 4.6 - Prob. 7WECh. 4.6 - Prob. 8WECh. 4.6 - Prob. 9WECh. 4.6 - Prob. 10WECh. 4.6 - Prob. 11WECh. 4.6 - Prob. 12WECh. 4.6 - Prob. 13WECh. 4.6 - Prob. 14WECh. 4.6 - Prob. 15WECh. 4.6 - Prob. 16WECh. 4.6 - Prob. 17WECh. 4.6 - Prob. 1MRECh. 4.6 - Prob. 2MRECh. 4.6 - Prob. 3MRECh. 4.6 - Prob. 4MRECh. 4.6 - Prob. 5MRECh. 4.6 - Prob. 6MRECh. 4.6 - Prob. 7MRECh. 4.6 - Prob. 8MRECh. 4.6 - Prob. 9MRECh. 4.6 - Prob. 10MRECh. 4.6 - Prob. 11MRECh. 4.7 - Prob. 1CECh. 4.7 - Prob. 2CECh. 4.7 - Prob. 3CECh. 4.7 - Prob. 4CECh. 4.7 - Prob. 5CECh. 4.7 - Prob. 6CECh. 4.7 - Prob. 7CECh. 4.7 - Prob. 8CECh. 4.7 - Prob. 9CECh. 4.7 - Prob. 10CECh. 4.7 - Prob. 11CECh. 4.7 - Prob. 1WECh. 4.7 - Prob. 2WECh. 4.7 - Prob. 3WECh. 4.7 - Prob. 4WECh. 4.7 - Prob. 5WECh. 4.7 - Prob. 6WECh. 4.7 - Prob. 7WECh. 4.7 - Prob. 8WECh. 4.7 - Prob. 9WECh. 4.7 - Prob. 10WECh. 4.7 - Prob. 11WECh. 4.7 - Prob. 12WECh. 4.7 - Prob. 13WECh. 4.7 - Prob. 14WECh. 4.7 - Prob. 15WECh. 4.7 - Prob. 16WECh. 4.7 - Prob. 17WECh. 4.7 - Prob. 18WECh. 4.7 - Prob. 19WECh. 4.7 - Prob. 20WECh. 4.7 - Prob. 21WECh. 4.7 - Prob. 22WECh. 4.7 - Prob. 23WECh. 4.7 - Prob. 24WECh. 4.7 - Prob. 25WECh. 4.7 - Prob. 26WECh. 4.7 - Prob. 27WECh. 4.7 - Prob. 28WECh. 4.7 - Prob. 29WECh. 4.7 - Prob. 1ST3Ch. 4.7 - Prob. 2ST3Ch. 4.7 - Prob. 3ST3Ch. 4.7 - Prob. 4ST3Ch. 4.7 - Prob. 5ST3Ch. 4.7 - Prob. 6ST3Ch. 4 - Prob. 1CRCh. 4 - Prob. 2CRCh. 4 - Prob. 3CRCh. 4 - Prob. 4CRCh. 4 - Prob. 5CRCh. 4 - Prob. 6CRCh. 4 - Prob. 7CRCh. 4 - Prob. 8CRCh. 4 - Prob. 9CRCh. 4 - Prob. 10CRCh. 4 - Prob. 11CRCh. 4 - Prob. 12CRCh. 4 - Prob. 13CRCh. 4 - Prob. 14CRCh. 4 - Prob. 15CRCh. 4 - Prob. 16CRCh. 4 - Prob. 17CRCh. 4 - Prob. 18CRCh. 4 - Prob. 19CRCh. 4 - Prob. 20CRCh. 4 - Prob. 1CTCh. 4 - Prob. 2CTCh. 4 - Prob. 3CTCh. 4 - Prob. 4CTCh. 4 - Prob. 5CTCh. 4 - Prob. 6CTCh. 4 - Prob. 7CTCh. 4 - Prob. 8CTCh. 4 - Prob. 9CTCh. 4 - Prob. 10CTCh. 4 - Prob. 11CTCh. 4 - Prob. 12CTCh. 4 - Prob. 13CTCh. 4 - Prob. 14CTCh. 4 - Prob. 15CTCh. 4 - Prob. 16CTCh. 4 - Prob. 17CTCh. 4 - Prob. 18CTCh. 4 - Prob. 19CTCh. 4 - Prob. 20CTCh. 4 - Prob. 1ARCh. 4 - Prob. 2ARCh. 4 - Prob. 3ARCh. 4 - Prob. 4ARCh. 4 - Prob. 5ARCh. 4 - Prob. 6ARCh. 4 - Prob. 7ARCh. 4 - Prob. 8ARCh. 4 - Prob. 9ARCh. 4 - Prob. 10ARCh. 4 - Prob. 11ARCh. 4 - Prob. 12ARCh. 4 - Prob. 13ARCh. 4 - Prob. 14ARCh. 4 - Prob. 15ARCh. 4 - Prob. 16ARCh. 4 - Prob. 17ARCh. 4 - Prob. 18ARCh. 4 - Prob. 19ARCh. 4 - Prob. 20ARCh. 4 - Prob. 21ARCh. 4 - Prob. 22ARCh. 4 - Prob. 23ARCh. 4 - Prob. 24ARCh. 4 - Prob. 25ARCh. 4 - Prob. 26ARCh. 4 - Prob. 27ARCh. 4 - Prob. 28ARCh. 4 - Prob. 29ARCh. 4 - Prob. 30ARCh. 4 - Prob. 31ARCh. 4 - Prob. 32ARCh. 4 - Prob. 33ARCh. 4 - Prob. 1CURCh. 4 - Prob. 2CURCh. 4 - Prob. 3CURCh. 4 - Prob. 4CURCh. 4 - Prob. 5CURCh. 4 - Prob. 6CURCh. 4 - Prob. 7CURCh. 4 - Prob. 8CURCh. 4 - Prob. 9CURCh. 4 - Prob. 10CURCh. 4 - Prob. 11CURCh. 4 - Prob. 12CURCh. 4 - Prob. 13CURCh. 4 - Prob. 14CURCh. 4 - Prob. 15CURCh. 4 - Prob. 16CURCh. 4 - Prob. 17CURCh. 4 - Prob. 18CUR

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