The Pythagorean Theorem states that the two legs squared will equal the hypotenuse squared.
Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Since we are given the length of the two legs and the hypotenuse, if we plug in the values they are equal, they are right triangles.
The hypotenuse is the side opposite from the right angle, which will be the longest side.
Let's plug in the values.
Triangle 1
[tex]a^2+b^2=c^2\\[/tex]
[tex]9^2+12^2=225\\15^2=225[/tex]
So the first triangle is a right triangle.
Triangle 2
[tex]a^2+b^2=c^2[/tex]
[tex]6^2+8^2=100\\10^2=100[/tex]
So the second triangle is also a right triangle.
Triangle 3
[tex]a^2+b^2=c^2[/tex]
[tex]2^2+4^2=20\\6^2=36[/tex]
So the third triangle is not a right triangle.
Hope this helped,
chikafujiwara
キズナミュージック♪
