Special Right Triangles Georgia Performance Standards for Mathematics 2 (MM2G1) Determine the lengths of sides of 30°-60°-90° and 45°-45°-90 triangles

Special Right Triangles 45, 45, 90 30, 60, 90

The name represents the degree measurements 45°, 45°, 90°30°, 60°, 90°

Today: Were just going to focus on 45°, 45°, 90° Triangles

Before we get into the math of 45°, 45°, 90° triangles… PAUSE Can anyone think of an example of a 45 °, 45 °, 90 ° triangle in daily life??

Any Sport Fans or Athletes?

Field Goal kicker

Any Sandwich eaters??

Do you cut your sandwiches in half?? If you do… then you would have two 45°, 45°, 90° sandwich halves.

Other Examples Paper Footballs American money Bridges Wheelchair ramps

Question: So… besides sports and sandwiches Whats so special about 45°, 45°, 90° triangles?? Well class, Im glad you asked!

45°,45°, 90° triangles They are the ONLY isosceles right triangle! – Which means – It is the only right triangle with TWO equal sides and TWO equal angles. – This is important when measuring the length of the sides

Recall: The Pythagorean Theorem states: If right triangle has sides of length a and b and hypotenuse of c, then a 2 + b 2 = c 2

In Reference to a 45°,45°, 90°, we see:

For every 45°,45°, 90° triangle 1

a

Important Facts to Remember:

Any Questions about 45°,45°, 90° Triangles?

Next Lesson 30°, 60°, 90° Triangles 2 1