In a triangle abc, ad is drawn perpendicular to bc. prove that ab2 - bd2 = ac2 - cd2.

Given: In triangle ABC , AD is drawn perpendicular to BC.

Since AD is drawn perpendicular to BC, it creates two right triangles: ADB and ADC.

Prove that:

Pythagoras triangle for right angle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

In a right angle triangle ADB;

                [By Pythagoras theorem]

or

                     .......[1]

Now, in right angle triangle ADC;

               [By Pythagoras theorem]

or we can write this as;

                   ......[2]

Substituting the equation [1] in [2] we get;

           hence proved!

easy its decreasing

step-by-step explanation:

because its top point is at the to of the graph on the left side (atleast from the veiw i see it) now if that top point wast in the lower part of the graph it would be increasing hope this have a nice day