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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 10.3, Problem 10E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

In Exercises 5 to 10, the real numbers a, b, c, and d are positive.

Consider the quadrilateral with vertices at R 0 ,   0 , S a ,   0 , T a ,   a , and V 0 ,   a . Explain why R S T V is a square.

Chapter 10.3, Problem 10E, In Exercises 5 to 10, the real numbers a, b, c, and d are positive. Consider the quadrilateral with

To determine

To explain:

RSTV is a square.

Explanation

The given diagram is shown below.

To prove RSTV is a square, we have to prove the following statement.

All sides are equal and parallel.

Now, we have to find the whether opposite sides are equal.

The distance between MN is equal to the distance between QP.

The distance between MQ is equal to the distance between NP.

Find the length of the side RS.

x1,y1=R0, 0

x2,y2=Sa, 0

Formula for distance between two points

dRS=x2-x12+y2-y12

Substituting the x and y co-ordinates

dRS=a-02+0-02

On solving this,

dRS=a2+02

dRS=a2

dRS=a

Then, find the length of the side ST.

x1,y1=Sa,0

x2,y2=Ta, a

Substituting the x and y co-ordinates

dST=a-a2+a-02

On solving this,

dST=02+a2

dST=a2

dST=a

Find the length of the side TV.

x1,y1=Ta, a

x2,y2=V0, a

Substituting the x and y co-ordinates

dTV=0-a2+a-a2

On solving this,

dTV=-a2+02

dTV=a2

dTV=a

Then, find the length of the side VR.

x1,y1=V0, a

x2,y2=R0, 0

Substituting the x and y co-ordinates

dVR=0-02+0-a2

On solving this,

dVR=02+-a2

dVR=a2

dRS=dST=dTV=dVR

Hence, the all the sides are equal

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