Question

1. In given figure DE // BC. Which of the following is true. ​

Answer 1

Answer:

In △ADE and △ABC

∠ADE=∠ABC (As DE∥BC Corresponding angles)

∠AED=∠ACB (As DE∥BC Corresponding angles)

∠DAE=∠BAC (common angle)

∴△ADE∼△ABC by AAA similarity.

If two triangles are similar, then their corresponding sides are proportional.

⇒

AB/AD

= BC/DE

7/3 = 14x

x=7

3×14

⇒x=6

Answer 2

Given :  In given figure DE || BC

To Find : Which of the following is true. ​

x = (a + b)/y

y = ax/(a + b)

x = ay/(a + b)

x/y = a/b

Solution:

in ΔADE  and ΔABC

∠D = ∠B    corresponding angle

∠E = ∠C    corresponding angle

∠A  = ∠A  common  angle

⇒ADE ~ ABC  ( Using AA or AAA similarity )

AE/AC  = DE/BC

=> a/(AE + AC)  = x/y

=> a/(a + b)  = x/y

=> x = ay/(a + b)

x = ay/(a + b)  is the correct option,

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