Question

Does Pythagorean and Theorem apply to the triangle ? How do you know ?

Answer 1

Yes, the Pythagorean Theorem applies specifically to right triangles. A right triangle is a triangle that has one angle measuring 90 degrees. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed with the formula:

\[
c^2 = a^2 + b^2
\]

where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.

You can confirm that a triangle is a right triangle by checking if it satisfies the Pythagorean theorem. If you measure the lengths of the three sides of a triangle and find that they satisfy this equation, then the triangle is a right triangle. If they do not satisfy the equation, then the triangle is not a right triangle.

For example, in a triangle with sides of lengths 3, 4, and 5, we can check:

\[
5^2 = 3^2 + 4^2
\]
\[
25 = 9 + 16
\]
\[
25 = 25
\]

Since the equation holds true, this triangle is a right triangle, and the Pythagorean theorem applies.