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 14.2, Problem 4E
To determine

To prove: that you can see all of yourself in a mirror that is only half as tall as you are.

Expert Solution & Answer
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Explanation of Solution

Given information:

The given statement is you can see all of yourself in a mirror that is only half as tall as you are.

Proof:

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 14.2, Problem 4E

Consider you are standing in front of a mirror of height FH and your height is AE .

Point C represents your eye, A represents top of your head, E represents foot, B is the mid-point between your eye and top of your head, D is the mid-point between your eye and foot, F is the bottom of the mirror, H is the top of the mirror and G is a point in the mirror parallel to your eyes.

Since,

AE=AB+BC+CD+DEAE=BC+BC+CD+CD   [AB=BC,CD=DE]AE=2(BC+CD)   (i)andHF=HG+GF       (ii)

In similar triangles CGF and CDF

CF is common sideCD=DFtherefore,CD=GF

In similar triangles BCH and CGH

CH is common sideBH=CGtherefore, BC=HG

Substitute the values of HG and GF in equation i.

HF=HG+GF       (ii)HF=BC+CD        [CD=GF,BC=HG]HF=AE2                [AE=2(BC+CD)]

Therefore,

It is proved thatyou can see all of yourself in a mirror that is only half as tall as you are.

Chapter 14 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

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