1. 5.1 Special Right Triangles

2. What you should already know…
Right triangles have one 90o angle
The longest side is called the HYPOTENUSE
It is directly across from the 90o
The other sides are called LEGS
Hypotenuse
LEG

3. a2 + b2 = c2 Pythagorean Theorem
The sides of a right triangle satisfy this theorem:
a2 + b2 = c2
Hypotenuse
LEG

4. Vocabulary 45-45-90 Triangle:
In a triangle, the hypotenuse is times as long as each leg.

5. Hints for 45-45-90 Leg to Hypotenuse: MULTIPLY by
Hypotenuse to Leg: DIVIDE by
Hypotenuse = LEG
LEG
LEG

6. Example 1:
Find the value of x.
a) b)

7. Vocabulary 30-60-90 Triangle:
In a triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg.

8. How do you know which is the shorter leg and which is the longer leg???
We know that the hypotenuse is directly across from the 90O angle.
The shorter leg is across from the smaller angle (30o)
The longer leg is across from the larger angle (60O)

9.
30o
Hypotenuse
Longer Leg
60o
Shorter Leg

10. You always want to work with the Shorter Leg…it makes it easier!
Hints for
Shorter Leg to Hypotenuse: MULTIPLY by 2
Hypotenuse to Shorter Leg: DIVIDE by 2
Shorter Leg to Longer Leg: MULTIPLY by
Longer Leg to Shorter Leg: DIVIDE by
You always want to work with the Shorter Leg…it makes it easier!

11. 30-60-90 Shorter Leg Longer Leg = Shorter Hypotenuse = 2Shorter 30o

12. Example 2:
Find the values of x and y.

13. You Try:
Find the value of each variable.
1) )

14. Homework
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