Question

AABC is an isosceles triangle in which AB =AC.
Side BA is produced to D such that AD = AB
(see Fig. 7.34). Show that BCD is a right angle.​

Answer 1

Answer:

As opposite angles of equal sides are equal

let angles B , ACB , ACD , D be x .

they are all angles in triangle BCD .

So their sum should be 180° .

X+X+X+X = 180°

4x =180°

X= 45°

as angle c is ACD + ACB

it will be 2x which is 90° .

So it is proved that triangle BCD is a right angled triangle .

HOPE IT IS HELPFUL TO ALL !!

Answer 2

Step-by-step explanation:

given - AB=AC

AC=AD

AB = AD

to prove - angleBCD is 90 degree

solution -

in triangle ABC

AB=AC ...(given)

angleABC=angleACB .........(isosceles traiangle theorem) ......1

in triangleACD

AC=AD .....(given)

angle ACD=angle ADC .....(isosceles triangle theorem) ......2

as AB=AC=AD .....(given)

thus,angle ABC=angleACB=angleACD=angleADC

that is angle DBC=angle ACB=angle ACD=angleBDC ......3

angle DBC+angle DCB+angle ACB+

angle ACD=180 ....(angle sum property of triangle)

by 3, all angles above are equal

lets consider all of them as x

x+x+x+x=180

4x=180

x = 45

thus, angle ACD and angle ACB = 45 ......4

angle ACD + angle ABC = angleBCD

by 4, angle BCD = 45 + 45

= 90

therefore triangle BCD is right angle triangle