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?
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 =