Learning Outcome: Learn to use the Pythagorean Theorem to identify right triangles.

How can we identify right angle triangles if the right angle symbol is not indicated? Is this a right angled triangle? 6cm 10cm 8cm

The Pythagorean Theorem states that when we have a right angle triangle and we are trying to find an unknown side length, using the formula a 2 + b 2 = c 2 will allow us to find an unknown side length. b2b2 c2c2 a2a2

We can use this information to identify a right angle triangle. If 3 side lengths are given, we add the square of both side lengths and if they equal the square of the hypotenuse we have a right triangle. Another way of saying this is that if the sum of the left side of the equal sign equals the right side of the equal sign, we have a right angled triangle.

LSRS = RS = 100 and LS = 100, therefore it is a right-angled triangle.

There are 3 types of triangles: 1. Acute – where all angles in the triangle are less than 90 o 2. Right – one of the angles in the triangle measures 90 o 3. Obtuse – at least one of the angles in the triangle is more than 90 o and less than 180 o

The acute, right and obtuse triangles in the diagrams have squares drawn on the sides of each triangle. Notice that when you compare the sum of the areas of the two smaller squares to the area of the largest square for each triangle, the Pythagorean Theorem only works for the right triangle. TriangleSum of Areas of Two Smaller Squares Area of Largest Square Acute = cm 2 Right = cm 2 Obtuse = cm 2

When the left side equals the right side of the equals sign, we call this a triplet or triad of Pythagorean (Pythagorean Triplet)

Example: 17, 22 and 39

Assignment: pg #3-15 Remember to attempt your quiz when you are done the lesson to test your understanding of the concepts