special right triangles georgia performance standards for mathematics 2 (mm2g1) determine the...

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

ED

F

The name represents the degree measurements

45°, 45°, 90° 30°, 60°, 90°

Today:We’re 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

Field Goal kicker

http://www.youtube.com/watch?v=xoI1-3rfyL8

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

What’s so special about 45°, 45°, 90° triangles??

Well class, I’m 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 a2 + b2 = c2

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

a2 + b2 = c2 (1) 2 + (1) 2 = c2

1 + 1 = c2

2 = c2 c =

For every 45°,45°, 90° triangle

√21

For every 45°,45°, 90° triangle

aa

Important Facts to Remember:

• 45°, 45°, 90° triangle– Isosceles triangles• 2 equal sides and 2 equal angels

– Length measurements of 1, 1,

– One of two special right triangles

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

Next Lesson

30°, 60°, 90° Triangles

2

1

√3