Question

if ABCD is a square, how many triangles in the given figure follow the Pythagorean law?

Answer 1

Answer:

4

Step-by-step explanation:

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Answer 2

In the given square ABCD, 8 different possible triangles follow Pythagorean law.

Step-by-step explanation:

Pythagorean law: "In a right-angled triangle the square of the hypotenuse is equal to the sum of squares of other two sides"

• Given the square ABCD.

• Let the length of the side of the square be a.

• AC and BD are diagonals of square ABCD intersecting each other at point O

• First, let us consider the ΔADC which follows Pythagorean law with the right angle D, length of side a, and hypotaneous $\sqrt{2} a$.
• Similarly, ΔABC, ΔDAB, and ΔDCB follow Pythagorean law with the length of side a and hypotaneous  $\sqrt{2} a$.
• Now let us consider the ΔAOB which follows Pythagorean law with right angle O, length of the side $\frac{a}{\sqrt{2}}$ , and hypotaneous a.
• Similarly, ΔBOC, ΔCOD, and ΔDOA follow Pythagorean law with a length of the side  $\frac{a}{\sqrt{2}}$  and hypotaneous a.

Thus there are the following 8 different possible triangles that follow Pythagorean law.