ABC & DBC are both isosceles trangle on a common base BC such that a & D  lie on the same side of BC. Are trangle ADC & ADB congruent? Which condition do you use? If angle BAC=40 & angle BDC = 100 degree, then find angle ADB?

Dear Student!

Here is the answer to your query.

Given : ABC and BDC are two isosceles triangles.

We know that 2 sides of the isosceles triangles are equal

⇒ AB = AC and BD = DC  ...(1)

In ΔADB and ΔADC

AB = AC    (from (1))

BD = DC    (from (1))

and AD = AD    (common)

This ΔADC ΔADB  (by SSS congruency criterion)

⇒ ∠ADB = ∠ADC  (by C. P. C. T)  ...(2)

Also ∠ADB + ∠ADC + ∠BDC = 360°

⇒ ∠ADB + ∠ADC + 100° = 360°

⇒ ∠ADB + ∠ADC = 360° – 100° = 260°

⇒ ∠ADB + ∠ADB = 260°  (from (2))

⇒ 2∠ADB = 260°

⇒ ∠ADB =

Cheers!