Question

state and prove the basis proportionality theorem​

Answer 1

Answer:

Let us now state the Basic Proportionality Theorem which is as follows: If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio

Step-by-step explanation:

It is helpful........

Answer 2

Step-by-step explanation:

Basic Proportionality Theorem states that, if a line is parallel to a side of a triangle which intersects the other sides into two distinct points,then the line divides those sides of the triangle in proportion.

Let ABC be the triangle.

The line l parallel to BC intersect AB at D and AC at E.

To prove

DB/AD = EC/AE

Join BE,CD

Draw EF⊥AB, DG⊥CA

Since EF⊥AB,

EF is the height of triangles ADE and DBE

Area of △ADE=1/2 × base × height= 1/2 AD×EF

Area of △DBE= 1/2 ×DB×EF

areaofΔDBE/areaofΔADE =1/2 ×DB×EF/1/2×AD×EF

= DB/AD........(1)

Similarly,

areaofΔDCE/areaofΔADE = 1/2×AE×DG/1/2/×EC×DG

= ECAE......(2)

But ΔDBE and ΔDCE are the same base DE and between the same parallel straight line BC and DE.

Area of ΔDBE= area of ΔDCE ....(3)

From (1), (2) and (3), we have

AD/DB = AE/AC

Hence proved.