Answer:
Option B - Pythagorean Theorem
Step-by-step explanation:
Given: ΔABC is a right triangle.
Prove: [tex]a^2 + b^2 = c^2[/tex]
Solution :
For the results we need to proof the Pythagoras theorem.
Refer the attached figure in the question.
Here, ABC is the triangle in which CD is the altitude from the point C.
Where, [tex]D\in AB[/tex]
Now,
Segment BC = a, segment CA = b, segment AB = c, segment CD = h, segment DB = x, segment AD = y
As, c over a equals a over y and c over b equals b over x
We get, y + x = c
By, Pieces of Right Triangles Similarity Theorem
[tex]\triangle ABC\sim \triangle ACD \\\Rightarrow \frac{a}{c}=\frac{y}{a}[/tex]
[tex]\triangle ABC\sim \triangle BCD\\\Rightarrow \frac{b}{x}=\frac{c}{b}[/tex]
By, Cross Product Property
[tex]\Rightarrow a^2=cy \text{ and } b^2=cx[/tex]
Substituting,
[tex]a^2 + b^2 = cy + cx[/tex]
By, Addition Property of Equality
[tex]a^2 + b^2 = c(y +x)[/tex]
[tex]a^2 + b^2 = c(c)[/tex]
[tex]a^2 + b^2 = c^2[/tex]
Hence Proved.
Now, We have seen that only Pythagorean Theorem is not the justification for the proof.
Therefore, Option B is correct.
