Question

If ML is parallel to BC and LN is parallel to DC. Prove that AM/AB=AN/AD

Answer 1

Answer:

Step 1:

Since ML//BC

∴ ∠AML = ∠ABC …. [corresponding angles] …. (i)

Consider ∆ AML and ∆ ABC, we have

∠MAL = ∠BAC ….. [common angle]

∠ AML = ∠ABC …. [from (i)]

∴ By AA similarity, ∆ AML ~ ∆ ABC

Since corresponding sides of similar triangles are proportional to each other.

∴ AM/AB = AL/AC ….. (ii)

Step 2:

Since LN//DC

∴ ∠ANL = ∠ADC …. [corresponding angles] …. (iii)

Consider ∆ ANL and ∆ ADC, we have

∠NAL = ∠DAC ….. [common angle]

∠ANL = ∠ADC …. [from (iii)]

∴ By AA similarity, ∆ ANL ~ ∆ ADC

Since corresponding sides of similar triangles are proportional to each other.

∴ AN/AD = AL/AC ….. (iv)

Step 3:

From (ii) & (iv), we get

AM/AB = AN/AD

Hence proved