Question

BD and CD bisect Angle ABC and Angle ACB respectively of Triangle ABC.Prove that Angle BDC = 90 0 + 1/2 Angle A.

Answer 1

FIRST PART OF YOUR ANSWER

by cpct;
angle BDE=CDE
(the angles named as 3)
in triangle DEC,
by angle sum property;
angleDEC +3+2=180
3+2=180-90
3+2=90____(equation 2)
2=90-3_____(equation 3)
in triangleAEC;
By angle sum property;
angleAEC+4+2+2=180
2(angle 2)+4=180-90
2(2)+4=90___(equation4)
(equation2)=(equation4)
3+2=2(2)+4
3-4=2(2)-2
3-4=2
from (equation 3)
3-4=90-3
2(3)=90+4
angleBDC=90+1/2(angle A)

hence proved

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please note that the numbers 1, 2, 3 and 4 denote angles named in the diagram