1. Special Right Triangles
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2. Special RightTriangles
There are two types of Special Right Triangles. Each one has a standard set of rules. These triangles show up on the SAT and every standardized test. 45 30 45 60

3. Special Right Triangles
Find the missing sides of each triangle.
Fill in the missing angle 45 90 45 x m =3 m =3 6 z w =4 45 45 45 45 y =6 4
Each triangle is Isosceles

4. Special Right Triangles
So, based on our examples, let’s come up with some shortcuts for the triangle… example: 45 45
Special Note:
You decide to multiply or divide based on whether the side you are going to is larger or smaller 6
hyp
leg 45 6
So how do you get from the leg to the hypotenuse?
SAME 45
leg

5. Special Right Triangles
Find x and y. Leave answers in SRF
Start by labeling sides. 45 y y
=16 10 x
Same
Same 45 x
=10

6. Special Right Triangles
Find x and y. Leave answers in SRF
Start by labeling sides. 45 6 x x
Same
Same 45 y y

7. Special Right Triangles
The triangle has its own rules… Let’s see if we can find x and y.
Find y using trigonometry and the 60 degree angle
Find x using the Pythagorean Theorem 30 y
=10 x 60 5

8. Special Right Triangles
So, based on our example, let’s come up with some shortcuts for triangles 30 30 10
Special Note:
You choose to multiply or divide based on whether the side you are going to is larger or smaller
hyp
Long leg 60 5 60
Short leg

9. Special Right Triangles
Fin x and y. Leave answers in SRF
Start by labeling sides. 30 30
Long Leg
Long Leg x 20 15
Hypotenuse x
Hypotenuse 60 60 y y
=10
Short Leg
Short Leg
Remember that you decide to multiply or divide based on whether you are going to a larger or smaller side

10. Special Right Triangles
Find the Area of the figure.
Area = (base)(height)
= (10)(height)
= (10)
square units 10 6 6 h 60 10
To find the height, we need to draw in a triangle and use our special triangle rules 6 h 60 3

11. Special Right Triangles
Find the Area of the Equilateral Triangle.
Area = ½ (base)(height)
= ½ (8)(height)
= ½ (8)
square units 8 8 h
To find the height, we need to draw in a triangle and use our special triangle rules 8 30
You can use the Pythagorean Theorem, but this is a triangle because the triangle above is equilateral.. 8 h 60 4