Question

prove
in an isosceles triangle ABC with AB is equal to AC, BD is perpendicular from B to the side AC prove that BD^2 - CD ^2 is equal to 2 CD. AD​

Answer 1

Answer:

Step-by-step explanation:

Given that : AB = AC AND BD IS PERPENDICULAR TO AC THEN;

IN TRIANGLE ABD

AB^2 - AD^2 = BD^2 --------- (1)

BC^2 - BD^2 = CD^2 --------- (2)

SUBTRACTING EQ 2 FROM 1

BD^2 - CD^2 = AB^2 - AD^2 - BC^2 + BD^2

BD^2 - CD^2 = AB^2 - AD^2 - BC^2 + (BC^2 - CD^2) ------- (BC^2 - CD^2 = BD^2)

BD^2 - CD^2 = AB^2 - AD^2 - CD^2 ---------(3)

AB = AC     (GIVEN)

AB = AD + CD

AB^2 = AD^2 + CD^2 + 2AD.CD ----------(4)

SUBSTITUTING THE VALUE IN EQ 3

BD^2 - CD^2 = AD^2 + CD^2 + 2AD.CD - AD^2 - CD^2

BD^2 - CD^2 = 2AD.CD

HENCE PROVED;

CHEERS