# Basic Geometry Theorem

**BASIC PROPORTIONALITY THEOREM**

**If a line is drawn parallel to one side of a triangle, the other two sides of the triangle are divided proportionally.**

Thus, in Fig. DE || BC, According to the above result

AD/DB = AE /EC

AD/DB = AE /EC

We can easily verify this by measuring AD, DB, AE and EC.

We state the converse of the above result as follows :

**If a line divides any two sides of a triangle in the same ratio, the line is parallelto third side of the triangle.**

Example:

Ans: AB/BD=AC/CE =>2/3=4/CE

=>CE =6 and AE = 10

try A tough one

In the above figure angle A is 30 degree and length of BC is 3 cm, then find out the length of

b. AB, BD

c. AC, CE

n/a

the theorem was gud but the question was incomplete or the data given was insufficent u cn only calculate the length of ab and ac...

n/a

Not exactly,

all the lengths can be calcualted as this is a right angle triangle

nah ....nt exactly all the lengths .... the lengths BD nd CE have to be confined with certain constraints .....as no such constraints is given the lengths BD CE nd DE cn acquire any possible length keeping the angle 30 degree nd the sides AB nd AC fixed accordingly ..... give it a try u wont be able to find any particular nd fixed length for BD CE nd DE there cn be infinite possibilities nd infinite probable lengths for the 3 sides even though there are right angled triangles in above fig.

n/a

My answers are

AB = 3 sqrt(3)

AD = 6 sqrt(3)

AC = 6

AE = 12

DE = 6

MY ANSWERS ARE

DE=3

AB = 3 sqrt(3)

AD = 6 sqrt(3)

AC=3

CE=3

That is pretty clear theorem. But I 'm cofused about the question posted. I could not come up with a solution. Could someone help me out with this.

Thanks in advance.