PRESENTATION TO SHOW

EXAMPLE- 1

Show that a median of

a triangle divides it into

two triangles of equal

areas.

Let ABC be a triangle and let AD be one of its medianssuppose, you wish to show area(ABD) = area(ACD) Since the formula for area involves altitude ,let us draw

AN┴BC.

Now area(ABD) = 1 ∕ 2 x base x altitude(of ∆ADB)

= 1 ∕ 2 x BD x AN

= 1 ∕ 2 x CD x AN(As BD = CD)

= 1 ∕ 2 x base x altitude(of ∆ACD)

= area(ACD)

EXAMPLE- 2

ABCD is a quadrilateral and BE||AC and also BE meets DC produced at E. Show that area of ∆ADE is equal to the area of the quadrilateral ABCD.

Solution:- In the given figure ∆BAC and ∆EAC lie on the same base

AC and between the same parallels AC and BE.

Therefore, area(BAC) = area(EAC)(two triangles on the same base and between the same parallels are equal in area)

So, area(BAC) +area(ADC) = area(EAC) + area(ADC)

(adding same areas on both sides)

area(ABCD) = area(ADE)