   Chapter 10.4, Problem 7E ### 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

# In Exercises 1 to 17, complete an analytic proof for each theorem.The line segments that join the midpoints of the consecutive sides of a quadrilateral from a parallelogram.

To determine

The analytic proof for the given theorem “The line segments that join the midpoints of the consecutive sides of a quadrilateral form a parallelogram”.

Explanation

Given theorem is,

The line segments that join the midpoints of the consecutive sides of a quadrilateral form a parallelogram

The above figure shows the quadrilateral ABCD.

R, S, T and V are the midpoints of the ides of the quadrilateral AB, BC, CD and AD respectively.

Now, joining the midpoints RS, ST, TV and VR as shown in the above figure.

The coordinate of the quadrilateral ABCD is A(0, 0), B(2a, 0),C(2b, 2c) and D(2d, 2e).

The midpoint of AB =R=0+2a2,0+02

R=2a2,0=a,0

The midpoint of BC =S=2a+2b2,0+2c2

S=2(a+b)2,c=a+b,c

The midpoint of CD =T=2d+2b2,2e+2c2

T=2(d+b)2,2(e+c)2=d+b,e+c

V=2d2,2e2=d,e

Determining the slopes as below,

mRS-=

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Simplify: 4854

Elementary Technical Mathematics

#### Minimize subject to C=24x+18y+24z 3x+2y+z4x+y+3z6x0,y0,z0

Finite Mathematics for the Managerial, Life, and Social Sciences

#### The length of the curve given by x = 3t2 + 2, y = 2t3, is:

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 