Question

State and Prove basic proportionality theorem.​

Answer 1

Answer:

Basic proportionality theorem: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio. and DE intersects AB and AC at D and E respectively. ... Hence, we can say that the basic proportionality theorem is proved.

Step-by-step explanation:

Hope this helps:)  ジョセフ

Answer 2

Answer:

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=

2

1

× base × height=

2

1

AD×EF

Area of △DBE=

2

1

×DB×EF

areaofΔDBE

areaofΔADE

=

2

1

×DB×EF

2

1

×AD×EF

=

DB

AD

Similarly

areaofΔDCE

areaofΔADE

=

2

1

×EC×DG

2

1

×AE×DG

=

EC

AE

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

DB

AD

=

EC

AE