Similar Triangles

 To solve a proportions  Cross multiply  Solve

1. Write the proportions for corresponding sides 2. Solve the proportion

The geometric mean of two numbers is the square root of the product of the numbers.

Find the geometric mean of the two numbers. Simplify your answer. 1.7 and 35

Right Triangles

a 2 + b 2 = c 2 c a b

Sin A = Cos A = Tan A =

Find the value of sine, cosine, and tangent ratios to the nearest hundredth.

If you know two sides and one angle:  To find the missing side use Pythagorean theorem: a 2 + b 2 = c 2  To find the two angles use inverse trigonometric functions: Angle = Sin -1 Angle = Cos -1 Angle = Tan -1

If you know two angles and one side:  To find the missing angle: Add the two angles and subtract from  To find the two missing sides use the trigonometric ratios. Sin angle = Cos angle = Tan angle =

Solve each triangle for all the missing information. Round your answer to the nearest tenth.

Circles

 Central Angle Angle = Arc  Inscribed Angle Angle = ½ Arc  Inside the circle Angle = ½ (sum of the arcs)  Outside the circle Angle = ½ (difference of the arcs)

Find the measure of the missing angle or arc.

 Inside the circle Part ∙ Part = Part ∙ Part  Outside the circle Outside ∙ Whole = Outside ∙ Whole E C A B D

Solve for x.

 C = 2  r B A

Find the length of arc BC. Leave your answer in terms of  7 in 40 o

 A =  r 2 P D C

Find the area of the shaded region. Leave your answer in terms of  7 in 30 0

Area of Polygons

 Circle  C = 2  r  A =  r 2  Squares  P = 4s  A = s 2  Rectangles  P = 2L + 2W  A = L W r s L W

 Parallelograms  P = 2b + 2 l  A = b h  Trapezoids  P = add up all 4 sides  A = ½ (b 1 + b 2 ) h  Triangles  P = a + b + c  A = ½ b h b l h b2b2 b1b1 h a c b

 P = 3s  A = ¼ s 2 √3 s

 Given side length and apothem  P = n s  A = n [ ½ (s)(a)] as

 Given side length only  P = n s  To find a   n 2. x = s/2 3. a = x/tan  4. A = n [ ½ (s)(a)] s 

Find the perimeter and area of each polygon. 1.

2.

Find the area of the regular polygons ft

Surface Area & Volume

 B = Area of the Base  Base is the shape not like the others Base does not mean the bottom shape Base is not one number it is an area (use the previous chapter)  P = Perimeter of the Base  h = height of the polyhedron  l = slant height of the polyhedron

 Prism  SA = 2B + Ph  V = Bh  Pyramid  SA = B + ½ P l  V = 1/3 B h l

 Cylinder  SA = 2  r  r h  V =  r 2 h  Cone  SA =  r 2 +  r l  V = 1/3  r 2 h r h l h r

 Sphere  SA = 4  r 2  V = 4/3  r 3 r

Find the surface area and volume of the right prism in 9 in 2 in

Find the surface area and volume of the right pyramid in 9 in