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