Chapter 8.1, Problem 33E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# Given △ A B C with midpoints M, N and P of the sides, explain why A A B C = 4 ⋅ A M N P .

To determine

To find:

AABC=4AMNP. In ABC with midpoint M, N and P of the sides,

Explanation

Given,

â–³ABC with midpoints M, N and P of the sides,

Let AB=a

BC=b and AC=c

P is the midpoint of AB,

Then AP=a2, and PB=a2

N is the midpoint of BC.

Then, BN=b2, and NC=b2

M is the midpoint of AC,

Then, AM=c2, and MC=c2

Thus, MNâˆ¥PB,Â NPâˆ¥AM,Â andÂ MPâˆ¥NC

(i.e.) MN=PB=a2

NP=AM=c2

MP=CN=b2

Now, the figure becomes,

From the figure, the dimensions of inscribed triabngles â–³MNP,Â â–³AMP,Â â–³PNB, and â–³NCM are same

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