ABC and DBC are both isosceles tringles on a common base BC such that A and D lie on the - Maths - Congruence of Triangles

Question

ABC and DBC are both isosceles tringles on a common base BC such
that A and D lie on the same side of Bc Are triangles ADB and ADC
congruent? Which condition do you use? If angle BAC = 40 degrees
and angle BDC = 100 degrees then find angle ADB

Harleen Birdi · Accepted Answer

Given: 2 triangles ABC and BDC having common base BC, AB = BD, AC = CD

Consider Î”ABC and Î”BCD, AB = BD (given) BC = BC (common) AC = CD (given) âˆ´ Î”ABC $≅$ Î”DBC,by SSS congruency Hence, âˆ 1 = âˆ 2 and âˆ 3 = âˆ 4 (cpct) â‡’ âˆ 5 = âˆ 6 But âˆ ABD may or may not be equal to âˆ ACD

ABC and DBC are both isosceles tringles on a common base BC such that A and D lie on the same side of Bc. Are triangles ADB and ADC congruent? Which condition do you use? If angle BAC = 40 degrees and angle BDC = 100 degrees then find angle ADB