Special Right Triangles

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Special Right Triangles Keystone Geometry

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Presentation transcript:

Special Right Triangles 45-45-90 & 30-60-90

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

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 45-45-90 triangle is Isosceles

Special Right Triangles So, based on our examples, let’s come up with some shortcuts for the 45-45-90 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

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

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

Special Right Triangles The 30-60-90 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

Special Right Triangles So, based on our example, let’s come up with some shortcuts for 30-60-90 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

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

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

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 30-60-90 triangle because the triangle above is equilateral.. 8 h 60 4