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 13, Problem 25CR
To determine

To prove: that ONQM is a parallelogram.

Expert Solution & Answer
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Explanation of Solution

Given information:

M is the middle point of RQ¯ and N is the middle point of OP¯ .

Formula used:

Distance between two points

  =(x2x1)2+(y2y1)2

Proof:

Since coordinates of points O, R, Q, and P are (0,0),(b,c),(b+a,c) and (a,0) respectively.

Coordinates of M

  =(b+b+a2,c+c2)

Coordinates of N

  =(0+a2,0)

Length of ON

  =(aa2)2+(0)=a2

Length of NQ

  =(a2(a+b))2+(0c)2=(b+a2)2+c2

Length of OM

  =(b+a20)2+(c0)2=(b+a2)2+c2

Length of MQ

  =(b+a2(a+b))2+(cc)2=a2

Here ON=MQ and NQ=OM that means opposite sides of the quadrilateral ONQM are congruent.

Therefore,

Thequadrilateral ONQM is a parallelogram.

Chapter 13 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

Ch. 13.1 - Prob. 11CECh. 13.1 - Prob. 12CECh. 13.1 - Prob. 1WECh. 13.1 - Prob. 2WECh. 13.1 - Prob. 3WECh. 13.1 - Prob. 4WECh. 13.1 - Prob. 5WECh. 13.1 - Prob. 6WECh. 13.1 - Prob. 7WECh. 13.1 - Prob. 8WECh. 13.1 - Prob. 9WECh. 13.1 - Prob. 10WECh. 13.1 - Prob. 11WECh. 13.1 - Prob. 12WECh. 13.1 - Prob. 13WECh. 13.1 - Prob. 14WECh. 13.1 - Prob. 15WECh. 13.1 - Prob. 16WECh. 13.1 - Prob. 17WECh. 13.1 - Prob. 18WECh. 13.1 - Prob. 19WECh. 13.1 - Prob. 20WECh. 13.1 - Prob. 21WECh. 13.1 - Prob. 22WECh. 13.1 - Prob. 23WECh. 13.1 - Prob. 24WECh. 13.1 - Prob. 25WECh. 13.1 - Prob. 26WECh. 13.1 - Prob. 27WECh. 13.1 - Prob. 28WECh. 13.1 - Prob. 29WECh. 13.1 - Prob. 30WECh. 13.1 - Prob. 31WECh. 13.1 - Prob. 32WECh. 13.1 - Prob. 33WECh. 13.1 - Prob. 34WECh. 13.1 - Prob. 35WECh. 13.1 - Prob. 36WECh. 13.1 - Prob. 37WECh. 13.1 - Prob. 38WECh. 13.1 - Prob. 39WECh. 13.1 - Prob. 40WECh. 13.1 - Prob. 41WECh. 13.1 - Prob. 42WECh. 13.1 - Prob. 43WECh. 13.1 - Prob. 44WECh. 13.1 - Prob. 45WECh. 13.1 - Prob. 3ECh. 13.2 - Prob. 1CECh. 13.2 - Prob. 2CECh. 13.2 - Prob. 3CECh. 13.2 - Prob. 4CECh. 13.2 - Prob. 5CECh. 13.2 - Prob. 6CECh. 13.2 - Prob. 7CECh. 13.2 - Prob. 8CECh. 13.2 - Prob. 1WECh. 13.2 - Prob. 2WECh. 13.2 - Prob. 3WECh. 13.2 - Prob. 4WECh. 13.2 - Prob. 5WECh. 13.2 - Prob. 6WECh. 13.2 - Prob. 7WECh. 13.2 - Prob. 8WECh. 13.2 - Prob. 9WECh. 13.2 - Prob. 10WECh. 13.2 - Prob. 11WECh. 13.2 - Prob. 12WECh. 13.2 - Prob. 13WECh. 13.2 - Prob. 14WECh. 13.2 - Prob. 15WECh. 13.2 - Prob. 16WECh. 13.2 - Prob. 17WECh. 13.2 - Prob. 18WECh. 13.2 - Prob. 19WECh. 13.2 - Prob. 20WECh. 13.2 - Prob. 21WECh. 13.2 - Prob. 22WECh. 13.2 - Prob. 23WECh. 13.2 - Prob. 24WECh. 13.2 - Prob. 25WECh. 13.2 - Prob. 26WECh. 13.2 - Prob. 27WECh. 13.2 - Prob. 28WECh. 13.2 - Prob. 29WECh. 13.2 - Prob. 30WECh. 13.2 - Prob. 31WECh. 13.2 - Prob. 32WECh. 13.2 - Prob. 33WECh. 13.2 - Prob. 34WECh. 13.2 - Prob. 1ARCh. 13.2 - Prob. 2ARCh. 13.2 - Prob. 3ARCh. 13.2 - Prob. 4ARCh. 13.2 - Prob. 5ARCh. 13.2 - Prob. 6ARCh. 13.2 - Prob. 7ARCh. 13.2 - Prob. 8ARCh. 13.2 - Prob. 9ARCh. 13.2 - Prob. 10ARCh. 13.2 - Prob. 11ARCh. 13.2 - Prob. 12ARCh. 13.2 - Prob. 13ARCh. 13.2 - Prob. 14ARCh. 13.2 - Prob. 15ARCh. 13.2 - Prob. 16ARCh. 13.2 - Prob. 17ARCh. 13.2 - Prob. 18ARCh. 13.2 - Prob. 19ARCh. 13.2 - Prob. 20ARCh. 13.2 - Prob. 21ARCh. 13.2 - Prob. 22ARCh. 13.2 - Prob. 23ARCh. 13.2 - Prob. 24ARCh. 13.3 - Prob. 1CECh. 13.3 - Prob. 2CECh. 13.3 - Prob. 3CECh. 13.3 - Prob. 4CECh. 13.3 - Prob. 5CECh. 13.3 - Prob. 6CECh. 13.3 - Prob. 7CECh. 13.3 - Prob. 8CECh. 13.3 - Prob. 9CECh. 13.3 - Prob. 10CECh. 13.3 - Prob. 11CECh. 13.3 - Prob. 1WECh. 13.3 - Prob. 2WECh. 13.3 - Prob. 3WECh. 13.3 - Prob. 4WECh. 13.3 - Prob. 5WECh. 13.3 - Prob. 6WECh. 13.3 - Prob. 7WECh. 13.3 - Prob. 8WECh. 13.3 - Prob. 9WECh. 13.3 - Prob. 10WECh. 13.3 - Prob. 11WECh. 13.3 - Prob. 12WECh. 13.3 - Prob. 13WECh. 13.3 - Prob. 14WECh. 13.3 - Prob. 15WECh. 13.3 - Prob. 16WECh. 13.3 - Prob. 17WECh. 13.3 - Prob. 18WECh. 13.3 - Prob. 19WECh. 13.3 - Prob. 20WECh. 13.3 - Prob. 21WECh. 13.3 - Prob. 22WECh. 13.3 - Prob. 23WECh. 13.4 - Prob. 1CECh. 13.4 - Prob. 2CECh. 13.4 - Prob. 3CECh. 13.4 - Prob. 4CECh. 13.4 - Prob. 5CECh. 13.4 - Prob. 6CECh. 13.4 - Prob. 7CECh. 13.4 - Prob. 8CECh. 13.4 - Prob. 1WECh. 13.4 - Prob. 2WECh. 13.4 - Prob. 3WECh. 13.4 - Prob. 4WECh. 13.4 - Prob. 5WECh. 13.4 - Prob. 6WECh. 13.4 - Prob. 7WECh. 13.4 - Prob. 8WECh. 13.4 - Prob. 9WECh. 13.4 - Prob. 10WECh. 13.4 - Prob. 11WECh. 13.4 - Prob. 12WECh. 13.4 - Prob. 13WECh. 13.4 - Prob. 14WECh. 13.4 - Prob. 15WECh. 13.4 - Prob. 16WECh. 13.4 - Prob. 17WECh. 13.4 - Prob. 18WECh. 13.4 - Prob. 19WECh. 13.4 - Prob. 20WECh. 13.4 - Prob. 21WECh. 13.4 - Prob. 22WECh. 13.4 - Prob. 23WECh. 13.4 - Prob. 24WECh. 13.4 - Prob. 25WECh. 13.4 - Prob. 26WECh. 13.4 - Prob. 27WECh. 13.4 - Prob. 28WECh. 13.4 - Prob. 29WECh. 13.4 - Prob. 30WECh. 13.4 - Prob. 31WECh. 13.4 - Prob. 32WECh. 13.4 - Prob. 33WECh. 13.4 - Prob. 34WECh. 13.4 - Prob. 1MRECh. 13.4 - Prob. 2MRECh. 13.4 - Prob. 3MRECh. 13.4 - Prob. 4MRECh. 13.4 - Prob. 5MRECh. 13.4 - Prob. 6MRECh. 13.4 - Prob. 7MRECh. 13.4 - Prob. 8MRECh. 13.4 - Prob. 9MRECh. 13.4 - Prob. 10MRECh. 13.4 - Prob. 11MRECh. 13.4 - Prob. 12MRECh. 13.5 - Prob. 1CECh. 13.5 - Prob. 2CECh. 13.5 - Prob. 3CECh. 13.5 - Prob. 4CECh. 13.5 - Prob. 5CECh. 13.5 - Prob. 6CECh. 13.5 - Prob. 7CECh. 13.5 - Prob. 8CECh. 13.5 - Prob. 9CECh. 13.5 - Prob. 10CECh. 13.5 - Prob. 1WECh. 13.5 - Prob. 2WECh. 13.5 - Prob. 3WECh. 13.5 - Prob. 4WECh. 13.5 - Prob. 5WECh. 13.5 - Prob. 6WECh. 13.5 - Prob. 7WECh. 13.5 - Prob. 8WECh. 13.5 - Prob. 9WECh. 13.5 - Prob. 10WECh. 13.5 - Prob. 11WECh. 13.5 - Prob. 12WECh. 13.5 - Prob. 13WECh. 13.5 - Prob. 14WECh. 13.5 - Prob. 15WECh. 13.5 - Prob. 16WECh. 13.5 - Prob. 17WECh. 13.5 - Prob. 18WECh. 13.5 - Prob. 19WECh. 13.5 - Prob. 20WECh. 13.5 - Prob. 21WECh. 13.5 - Prob. 22WECh. 13.5 - Prob. 23WECh. 13.5 - Prob. 24WECh. 13.5 - Prob. 1ST1Ch. 13.5 - Prob. 2ST1Ch. 13.5 - Prob. 3ST1Ch. 13.5 - Prob. 4ST1Ch. 13.5 - Prob. 5ST1Ch. 13.5 - Prob. 6ST1Ch. 13.5 - Prob. 7ST1Ch. 13.5 - Prob. 8ST1Ch. 13.5 - Prob. 9ST1Ch. 13.5 - Prob. 10ST1Ch. 13.5 - Prob. 11ST1Ch. 13.5 - Prob. 12ST1Ch. 13.5 - Prob. 13ST1Ch. 13.5 - Prob. 14ST1Ch. 13.5 - Prob. 15ST1Ch. 13.6 - Prob. 1CECh. 13.6 - Prob. 2CECh. 13.6 - Prob. 3CECh. 13.6 - Prob. 4CECh. 13.6 - Prob. 5CECh. 13.6 - Prob. 6CECh. 13.6 - Prob. 7CECh. 13.6 - Prob. 8CECh. 13.6 - Prob. 9CECh. 13.6 - Prob. 10CECh. 13.6 - Prob. 11CECh. 13.6 - Prob. 12CECh. 13.6 - Prob. 13CECh. 13.6 - Prob. 1WECh. 13.6 - Prob. 2WECh. 13.6 - Prob. 3WECh. 13.6 - Prob. 4WECh. 13.6 - Prob. 5WECh. 13.6 - Prob. 6WECh. 13.6 - Prob. 7WECh. 13.6 - Prob. 8WECh. 13.6 - Prob. 9WECh. 13.6 - Prob. 10WECh. 13.6 - Prob. 11WECh. 13.6 - Prob. 12WECh. 13.6 - Prob. 13WECh. 13.6 - Prob. 14WECh. 13.6 - Prob. 15WECh. 13.6 - Prob. 16WECh. 13.6 - Prob. 17WECh. 13.6 - Prob. 18WECh. 13.6 - Prob. 19WECh. 13.6 - Prob. 20WECh. 13.6 - Prob. 21WECh. 13.6 - Prob. 22WECh. 13.6 - Prob. 23WECh. 13.6 - Prob. 24WECh. 13.6 - Prob. 25WECh. 13.6 - Prob. 26WECh. 13.6 - Prob. 27WECh. 13.6 - Prob. 28WECh. 13.6 - Prob. 29WECh. 13.6 - Prob. 30WECh. 13.6 - Prob. 31WECh. 13.6 - Prob. 32WECh. 13.6 - Prob. 33WECh. 13.6 - Prob. 34WECh. 13.6 - Prob. 35WECh. 13.6 - Prob. 36WECh. 13.6 - Prob. 37WECh. 13.6 - Prob. 38WECh. 13.6 - Prob. 39WECh. 13.6 - Prob. 1CCh. 13.7 - Prob. 1CECh. 13.7 - Prob. 2CECh. 13.7 - Prob. 3CECh. 13.7 - Prob. 4CECh. 13.7 - Prob. 5CECh. 13.7 - Prob. 6CECh. 13.7 - Prob. 7CECh. 13.7 - Prob. 8CECh. 13.7 - Prob. 9CECh. 13.7 - Prob. 10CECh. 13.7 - Prob. 11CECh. 13.7 - Prob. 12CECh. 13.7 - Prob. 13CECh. 13.7 - Prob. 14CECh. 13.7 - Prob. 1WECh. 13.7 - Prob. 2WECh. 13.7 - Prob. 3WECh. 13.7 - Prob. 4WECh. 13.7 - Prob. 5WECh. 13.7 - Prob. 6WECh. 13.7 - Prob. 7WECh. 13.7 - Prob. 8WECh. 13.7 - Prob. 9WECh. 13.7 - Prob. 10WECh. 13.7 - Prob. 11WECh. 13.7 - Prob. 12WECh. 13.7 - Prob. 13WECh. 13.7 - Prob. 14WECh. 13.7 - Prob. 15WECh. 13.7 - Prob. 16WECh. 13.7 - Prob. 17WECh. 13.7 - Prob. 18WECh. 13.7 - Prob. 19WECh. 13.7 - Prob. 20WECh. 13.7 - Prob. 21WECh. 13.7 - Prob. 22WECh. 13.7 - Prob. 23WECh. 13.7 - Prob. 24WECh. 13.7 - Prob. 25WECh. 13.7 - Prob. 26WECh. 13.7 - Prob. 27WECh. 13.7 - Prob. 28WECh. 13.7 - Prob. 29WECh. 13.7 - Prob. 30WECh. 13.7 - Prob. 31WECh. 13.7 - Prob. 32WECh. 13.7 - Prob. 33WECh. 13.7 - Prob. 34WECh. 13.7 - Prob. 35WECh. 13.7 - Prob. 36WECh. 13.7 - Prob. 37WECh. 13.7 - Prob. 38WECh. 13.7 - Prob. 39WECh. 13.8 - Prob. 1CECh. 13.8 - Prob. 2CECh. 13.8 - Prob. 3CECh. 13.8 - Prob. 4CECh. 13.8 - Prob. 5CECh. 13.8 - Prob. 6CECh. 13.8 - Prob. 1WECh. 13.8 - Prob. 2WECh. 13.8 - Prob. 3WECh. 13.8 - Prob. 4WECh. 13.8 - Prob. 5WECh. 13.8 - Prob. 6WECh. 13.8 - Prob. 7WECh. 13.8 - Prob. 8WECh. 13.8 - Prob. 9WECh. 13.8 - Prob. 10WECh. 13.8 - Prob. 11WECh. 13.8 - Prob. 12WECh. 13.8 - Prob. 13WECh. 13.9 - Prob. 1CECh. 13.9 - Prob. 2CECh. 13.9 - Prob. 3CECh. 13.9 - Prob. 4CECh. 13.9 - Prob. 5CECh. 13.9 - Prob. 1WECh. 13.9 - Prob. 2WECh. 13.9 - Prob. 3WECh. 13.9 - Prob. 4WECh. 13.9 - Prob. 5WECh. 13.9 - Prob. 6WECh. 13.9 - Prob. 7WECh. 13.9 - Prob. 8WECh. 13.9 - Prob. 9WECh. 13.9 - Prob. 10WECh. 13.9 - Prob. 11WECh. 13.9 - Prob. 12WECh. 13.9 - Prob. 13WECh. 13.9 - Prob. 14WECh. 13.9 - Prob. 1ST2Ch. 13.9 - Prob. 2ST2Ch. 13.9 - Prob. 3ST2Ch. 13.9 - Prob. 4ST2Ch. 13.9 - Prob. 5ST2Ch. 13.9 - Prob. 6ST2Ch. 13.9 - Prob. 7ST2Ch. 13.9 - Prob. 8ST2Ch. 13.9 - Prob. 9ST2Ch. 13.9 - Prob. 1AECh. 13.9 - Prob. 2AECh. 13.9 - Prob. 3AECh. 13.9 - Prob. 4AECh. 13.9 - Prob. 1BECh. 13.9 - Prob. 2BECh. 13.9 - Prob. 3BECh. 13.9 - Prob. 4BECh. 13.9 - Prob. 5BECh. 13.9 - Prob. 6BECh. 13.9 - Prob. 7BECh. 13.9 - Prob. 8BECh. 13.9 - Prob. 9BECh. 13.9 - Prob. 10BECh. 13.9 - Prob. 11BECh. 13.9 - Prob. 12BECh. 13.9 - Prob. 13BECh. 13.9 - Prob. 14BECh. 13.9 - Prob. 15BECh. 13.9 - Prob. 16BECh. 13 - Prob. 1CRCh. 13 - Prob. 2CRCh. 13 - Prob. 3CRCh. 13 - Prob. 4CRCh. 13 - Prob. 5CRCh. 13 - Prob. 6CRCh. 13 - Prob. 7CRCh. 13 - Prob. 8CRCh. 13 - Prob. 9CRCh. 13 - Prob. 10CRCh. 13 - Prob. 11CRCh. 13 - Prob. 12CRCh. 13 - Prob. 13CRCh. 13 - Prob. 14CRCh. 13 - Prob. 15CRCh. 13 - Prob. 16CRCh. 13 - Prob. 17CRCh. 13 - Prob. 18CRCh. 13 - Prob. 19CRCh. 13 - Prob. 20CRCh. 13 - Prob. 21CRCh. 13 - Prob. 22CRCh. 13 - Prob. 23CRCh. 13 - Prob. 24CRCh. 13 - Prob. 25CRCh. 13 - Prob. 1CTCh. 13 - Prob. 2CTCh. 13 - Prob. 3CTCh. 13 - Prob. 4CTCh. 13 - Prob. 5CTCh. 13 - Prob. 6CTCh. 13 - Prob. 7CTCh. 13 - Prob. 8CTCh. 13 - Prob. 9CTCh. 13 - Prob. 10CTCh. 13 - Prob. 11CTCh. 13 - Prob. 12CTCh. 13 - Prob. 13CTCh. 13 - Prob. 14CTCh. 13 - Prob. 15CTCh. 13 - Prob. 16CTCh. 13 - Prob. 17CTCh. 13 - Prob. 18CTCh. 13 - Prob. 19CTCh. 13 - Prob. 20CTCh. 13 - Prob. 21CTCh. 13 - Prob. 1CURCh. 13 - Prob. 2CURCh. 13 - Prob. 3CURCh. 13 - Prob. 4CURCh. 13 - Prob. 5CURCh. 13 - Prob. 6CURCh. 13 - Prob. 7CURCh. 13 - Prob. 8CURCh. 13 - Prob. 9CURCh. 13 - Prob. 10CURCh. 13 - Prob. 11CURCh. 13 - Prob. 12CURCh. 13 - Prob. 13CURCh. 13 - Prob. 14CURCh. 13 - Prob. 15CURCh. 13 - Prob. 16CURCh. 13 - Prob. 17CUR

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