Alyssa plans to use four triangles like the one shown to form a diamond shape 6 cm 3 cm 4 cm for her plan to work the triangle must be a right triangle determine whether the triangle is a right triangle is the triangle a right triangle or is it not a right triangle
To determine whether the triangle is a right triangle, we need to check if it satisfies the Pythagorean theorem. 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.
Let's label the sides of the triangle as follows:
- The longest side (opposite the right angle) with length 6 cm is the hypotenuse.
- The other two sides have lengths 3 cm and 4 cm.
Now, let's apply the Pythagorean theorem:
(3 cm)^2 + (4 cm)^2 = (6 cm)^2
9 cm^2 + 16 cm^2 = 36 cm^2
25 cm^2 = 36 cm^2
Since 25 cm^2 is not equal to 36 cm^2, the triangle does not satisfy the Pythagorean theorem. Therefore, the triangle is not a right triangle.