Question

In ABC, if DE ll BC then prove that AD/AB=AE/AC​

Answer 1

Answer:

Step-by-step explanation:

ABC is a triangle and DE is parallel to BC.

‌‌ ‌‌‌‌‌ :

AD/DB = AE/EC

‌‌‌‌‌‌‌‌‌‌‌‌ :

* draw DM perpendicular to AC.

* And draw EN perpendicular to AB.

* Join BE and CD.

‌‌‌‌‌ :

Area of triangle =1/2bh

In ADE =1/2 (AD)(EN),

In BDE =1/2 (DB) (EN).

Ar. Of ADE = 1/2 (AE)(DM)

Ar. Of Dec = 1/2 (EC) (DM).

.'. Ar.(ADE)/ Ar. (BDE)= 1/2AD* EN/ 1/2 DB* EN = AD / DB. - eq1⃣

Ar. ADE / are. DEC = 1/2 AE * DM/ 1/2 EC *DM = AC /EC. - eq✌️

BDE & DEC are lie on the same base and between the same parallels.

So, Ar. BDE = Ar. DEC

From eq one1⃣ and two✌️,

ᴀᴅ /ᴅʙ = ᴀᴇ /ᴇᴄ