Question

state and prove BPT​

Answer 1

Answer:

Statement : If a line passing through two sides of triangle then it os parallel to third side then divides other two sides in same ratio.

In ΔADE (Baes AD)

Area of triangle =

2

1

.AD.ME _______ (1)

Again in ΔADE (Base AE)

ar.(ΔADE)=

2

1

.AE.ND ________ (2)

In ΔBDE (Base BD)

ar.(ΔBDE)=

2

1

.DB.ME ________ (3)

In ΔDEC (Base EC)

ar.(ΔDEC)=

2

1

.EC.ND ________ (4)

Equation (1) & (3)

ar.ΔBDE

ar.ΔADE

=

2

1

.DB.ME

2

1

.AD.ME

ar.ΔBDE

arΔADE

=

DB

AD

_______ (5)

Now equation (2) & (4)

ar.(ΔDEC)

ar.(ΔADE)

=

2

1

.EC.ND

2

1

.AE.ND

ΔDEC

ar.(ΔADE)

=

EC

AE

_______ (6)

By theorem,

ar.(ΔBDE)=ar.(ΔDEC)

ar.(ΔBDC)

ar.(ΔADE)

=

ar.(ΔDEC)

ar.(ΔADE)

=

BD

AD

ar.(ΔDEC)

ar.(ΔADE)

=

BD

AD

________ (7)

By equation (6) & (7)

There L.H.S is same and R.H.S is same.

EC

AE

=

BD

AD

∴

DB

AD

=

EC

AE

Step-by-step explanation:

hope it helps you!!

Answer 2

Answer:

$answer$

Step-by-step explanation:

$Statement : If a line passing through two sides of triangle then it os parallel to third side then divides other two sides in same ratio.</p><p></p><p>In ΔADE (Baes AD)</p><p></p><p>Area of triangle = 21.AD.ME _______ (1)</p><p></p><p>Again in ΔADE (Base AE)</p><p></p><p>ar.(ΔADE)=21.AE.ND ________ (2)</p><p></p><p>In ΔBDE (Base BD)</p><p></p><p>ar.(ΔBDE)=21.DB.ME ________ (3)</p><p></p><p>In ΔDEC (Base EC)</p><p></p><p>ar.(ΔDEC)=21.EC.ND ________ (4)</p><p></p><p>Equation (1) & (3)</p><p></p><p>ar.ΔBDEar.ΔADE=21.DB.ME21.AD.ME</p><p></p><p>ar.ΔBDEarΔADE=DBAD _______ (5)</p><p></p><p>Now equation (2) & (4)</p><p></p><p>ar.(ΔDEC)ar.(ΔADE)=21.EC.ND21.AE.ND</p><p></p><p>ΔDECar.(ΔADE)=ECAE _______ (6)</p><p></p><p>By theorem,</p><p></p><p>ar.(ΔBDE)=ar.(ΔDEC)</p><p></p><p>ar.(ΔBDC)ar.(ΔADE)=ar.(ΔDEC)ar.(ΔADE)=BDAD</p><p></p><p></p><p>$

I hope it helps u ☺️...........