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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 5.6, Problem 34E
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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
Problem 38E
Problem 39E
Problem 40E
BuyFindarrow_forward

Elementary Geometry for College St...

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

Use Exercise 33 and the following drawing to complete the proof of this theorem: “The length of the median of a trapezoid is one-half the sum of the lengths of the two bases”.

Given: Trapezoid A B C D with median M N ¯ Chapter 5.6, Problem 34E, Use Exercise 33 and the following drawing to complete the proof of this theorem: The length of the , example 1
Prove: M N = 1 2 ( A B + C D )

33. Use Theorem 5.6.1 and the drawing to complete the proof of this theorem: “If a line is parallel to one side of a triangle and passes through the midpoint of a second side, then it will pass through the midpoint of the third side.”

Given: Δ R S T with M the midpoint of R S ; ¯ M N ↔ ∥ S T ¯ Chapter 5.6, Problem 34E, Use Exercise 33 and the following drawing to complete the proof of this theorem: The length of the , example 2
Prove: N is the midpoint of R T ¯

To determine

To prove:

MN=12(AB+CD).

Explanation

Given:

We need to prove, “The length of the median of a trapezoid is one-half the sum of the lengths of the two bases”.

In a trapezoid ABCD, MN¯ is the median.

Property used:

Means-Extremes Property:

In a proportion, the product of the means equals the product of the extremes; that is, if ab=cd (where b≠0 and d≠0), then a⋅d=b⋅c.

If a line is parallel to one side of a triangle and intersects other two sides, then it divides these sides proportionally.

Proof:

Consider a trapezoid ABCD.

Given that MN¯ is the median.

We know that the median of the trapezoid is parallel to each base.

MN¯∥AB¯∥CD¯

We know that, if a line is parallel to one side of a triangle and passes through the midpoint of a second side, then it will pass through the midpoint of the third side

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