
Remember the pattern for right triangles:
Area of small square
+
Area of medium square
=
Area of large square
a) 3 in. , 5 in., and 8 in.
9 + 25 = 64
34 ≠ 64 not a right triangle
b) 3 m, 4 m, and 5 m
9 + 16 = 25
25 = 25 right triangle
c) 4 cm, 6 cm, and 8 cm
16 + 36 = 64
52 ≠ 64 not a right triangle
9 + 34 = ?
? = 43
8 + 12 = ?
? = 20
10 + ? = 25
? = 15

The relationship that we have discovered
between the sides of right triangles is
called the Pythagorean Theorem.

It allows us to determine if a triangle is a
right triangle and to find missing side
lengths when we know that the triangle
is a right triangle.

legs =
› the sides that create the right angle
› “hold up” the right angle like legs to a table
› the two shorter sides
leg
leg

hypotenuse =
› the side across from the right angle
› does not touch the right angle
› the longest side of the triangle
hypotenuse


area of small square + area of
medium square = area of large square
leg² + leg² = hypotenuse²
or
a² + b² = c²
x
13 cm
5 cm
5² + x² = 13²
25 + x² = 169
-25
-25
x² = 144
𝑥 2 = 144
x = 12
12 cm

Don’t forget to identify the legs and
hypotenuse

Plug the values into the formula

Solve

Get a star after each row is completed