Question

If a lines drawn paralel the one of a triangle to inrrset the to rides in distincet point the other to rides are dividecil in the same ratio

Answer 1

Step-by-step explanation:

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. Given: In ∆ABC , which intersects AB and AC at D and F respectively.

Given:

DE∣∣BC

To prove that:

AE

EC

=

AD

BD

Proof:

∠AED=∠ACB Corresponding angles

∠ADE=∠ABC Corresponding angles

∠EAD is common to both the triangles

⇒ΔAED∼ΔACB by AAA similarity

⇒

AE

AC

=

AD

AB

⇒

AE

AE+EC

=

AD

AD+BD

⇒

AE

EC

=

AD

BD