It is past due! prove the pythagorean theorem using similar triangles. the pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse. be sure to create and name the appropriate geometric figures.

Explanation:

First we consider ΔABC and ΔBCD,

∠C=∠C  (common)

∠B=∠D=

So, ΔABC ≈ ΔBCD (By AA similarity rule )

So by taking corresponding sides in ratios we get

Now

             -------- Eqn (1)

Similarly,

We consider ΔABD and ΔABC

∠A=∠A (Commom)

∠B=∠D=

So,

ΔABD ≈ ΔABC (By AA similarity rule )

So by taking corresponding sides in ratios we get

Now,

             --------Eqn (2)

By Adding both the equation we get

Hence, we proved the pythagorean theorem by using similarity of triangle.

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.