17) in the given figure, if AB=AC, ABAD = CAE than prove that LADE is

1.	17) in the given figure, if AB=AC, ABAD = CAE than prove that LADE is an isosceles triangle.ARC DR R
Answer» Given :AB=AC Thus <ACB = <ABC (as angles opposite to equal sides are equal) Also, <BAD = <CAE ----- (1)<ABC = <ACB Hence, <ABD = <ACE ----(2)Adding (1) + (2) <BAD + <ABD = <CAE + <ACESince, external angle of a triangle is equal to the sum of two opposite internal angles. <ADE = <BAD + <ABD and <AED = <CAE + <ACE Therefore, <ADE = <AED Hence, two angles are equal in the triangle ADE and it can be said to be an isosceles triangle. Hence proved

17) in the given figure, if AB=AC, ABAD = CAE than prove that LADE is an isosceles triangle.ARC DR R

Answer»

Given :AB=AC Thus <ACB = <ABC (as angles opposite to equal sides are equal)

Also, <BAD = <CAE ----- (1)<ABC = <ACB

Hence, <ABD = <ACE ----(2)Adding (1) + (2)

<BAD + <ABD = <CAE + <ACESince, external angle of a triangle is equal to the sum of two opposite internal angles.

<ADE = <BAD + <ABD and <AED = <CAE + <ACE

Therefore, <ADE = <AED

Hence, two angles are equal in the triangle ADE and it can be said to be an isosceles triangle.

Hence proved