Question

state and prove Basic proportional theorem​

Answer 1

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 DBAD=ECAE

Join BE,CD

Draw EF⊥AB, DG⊥CA

Since EF⊥AB,

EF is the height of triangles ADE and DBE

Area of △ADE=21× base × height=21AD×EF

Area of △DBE=21×DB×EF

areaofΔDBEareaofΔADE=21×DB×EF21×AD×EF=DBAD          ........(1)

Similarly,

areaofΔDCEareaofΔADE=21×EC×DG