Question

Given: ΔABC is a right triangle.

Answer 1

D. The Cross Product Property. This Property has nothing to do with a right triangle, and it deals with the products of cross multiplied numbers, and nothing to do with addition.

Answer 2

Answer:

Option B - Pythagorean Theorem

Step-by-step explanation:

Given: ΔABC is a right triangle.

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

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, $D\in AB$

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

$\triangle ABC\sim \triangle ACD \\\Rightarrow \frac{a}{c}=\frac{y}{a}$

$\triangle ABC\sim \triangle BCD\\\Rightarrow \frac{b}{x}=\frac{c}{b}$

By, Cross Product Property

$\Rightarrow a^2=cy \text{ and } b^2=cx$

Substituting,

$a^2 + b^2 = cy + cx$

By, Addition Property of Equality

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

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

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

Hence Proved.

Now, We have seen that only Pythagorean Theorem is not the justification for the proof.

Therefore, Option B is correct.