Question

Given: ΔABC is a right triangle.

Answer 1

Answer: Pythagorean Theorem is not the justification for the proof.

Step-by-step explanation:

We can get the right answer with help of the below proof of Pythagoras theorem,

Since, Here ABC is the triangle in which CD is the altitude from the point C.

Where,  $D\in AB$ ( shown in figure)

Here, segment BC = a, segment CA = b, segment AB = c, segment CD = h

segment DB = y , segment AD = x  

y + x = c ( c over a equals a over y and c over b equals b over x)

Since, $\triangle ABC\sim \triangle ACD$ ⇒ a/c=y/a and $\triangle ABC\sim \triangle BCD$⇒  b/x=c/b ( Pieces of Right Triangles Similarity Theorem)

⇒ a^2=cy and b^2=cx  (  Cross Product Property)

$a^2 + b^2 = cy + b2$ (Addition Property of Equality)

$a^2 + b^2 = cy + cx$  

$a^2 + b^2 = c(y + x)$  

$a^2 + b^2 = c(c)$

$a^2 + b^2 = c^2$

Answer 2

Pythagorean Theorum since that is what you are trying to prove.