   Chapter 10.CR, Problem 20CR ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

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

# Show that quadrilateral R S T V with vertices R - 5 ,   - 3 , S 1 ,   - 11 , T 7 ,   - 6 and V 1 ,   2 is a parallelogram.

To determine

To prove:

The quadrilateral RSTV with vertices R-5, -3, S1, -11, T7, -6 and V1, 2 is a parallelogram.

Explanation

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

Both pairs of opposite sides are parallel.

Find the slope of RS.

x1,y1=R-5, -3

x2,y2=S1, -11

Formula for slope joining the line segment.

Slope is denoted by m.

m=y2-y1x2-x1

Here x1x2

Substituting the x and y co-ordinates.

mRS-=-11--31--5

mRS-=-11+31+6

mRS-=-86

Cancelling the common factors,

mRS-=-43

Then, find the slope of ST.

x1,y1=S1, -11

x2,y2=T7, -6

Substituting the x and y co-ordinates.

mST-=-6--117-1

mST-=-6+116

mST-=56

Find the slope of TV

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