Area of the equilateral triangle, Mathematics

Area of the equilateral triangle:

600_Area of the equilateral triangle1.png

Given : D, E, F are the mind points of BC, CA, AB.
R.T.P. : We have to determine the ratio of the area of of triangle DEF and triangle ABC.
Proof : F is the mid point of AB.
D is the mid point of BC.

FD||AC => FD||AE 

Similarly ED||AF
FE||BD
 AFDE is a parallelogram.
∠A = ∠D (Opposite angles in a parallelogram)

Similarly BDEF is a parallelogram.
∠B = ∠E

In ΔABC, ΔDEF

∠A =∠D proved

∠B =∠E proved

ΔABC ~ ΔDEF (A. A similarity)

2011_Area of the equilateral triangle.png 

Ratio of the areas of triangle DEF and triangle ABC = 1 : 4

 

 

Posted Date: 9/3/2012 5:46:26 AM | Location : United States







Related Discussions:- Area of the equilateral triangle, Assignment Help, Ask Question on Area of the equilateral triangle, Get Answer, Expert's Help, Area of the equilateral triangle Discussions

Write discussion on Area of the equilateral triangle
Your posts are moderated
Related Questions
I am less than 100 the sum of my digits is 4 half of me is an odd number

INTRODUCTION : Most of us, when planning the first mathematical experience for three-year olds, think in terms of helping them memorise numbers from 1 to 20. We also teach them to

What is Slope of a Line ? A line can have a "steep" slope or a "gradual" slope. slope = rise/run The "rise" is the distance going up or down. The "run" is the distance goin

a business is owned by three people.the first owns 1/12 of the business and the second owns 1/6 of the business. what fractional part of the business is owned by the third person

Rate of Change : The first interpretation of derivative is rate of change.  It was not the primary problem which we looked at in the limit chapter, however it is the most signific

Derivatives of Exponential and Logarithm Functions : The next set of functions which we desire to take a look at are exponential & logarithm functions. The most common exponentia

Discuss the role research would play during your decision making

A certain flight arrives on time 78% of the time. Suppose 1000 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that a)

If tanx+secx=sqr rt 3, 0 Ans) sec 2 x=(√3-tanx) 2 1+tan 2 x=3+tan 2 x-2√3tanx 2√3tanx=2 tanx=1/√3 x=30degree