Geometry

Chapter 9 Material

Basic Terms Point Segment Line Ray Angle

Angle Terms Vertex Sides Names Measures: Decimal Degrees Degrees, Minutes, Seconds A V B

Angle Measure Convert 32.5˚ to D˚M’S”. Convert 95.265˚ to D˚M’S”. A full revolution is _____ degrees.

Types of Angles Acute (< 90˚) Right (= 90˚) Obtuse (> 90˚) Straight (= 180˚)

Line Relationships Intersecting Perpendicular Parallel Skew

Angle Relationships Adjacent Vertical Complementary (sum is 90˚) Supplementary (sum is 180˚) 137˚ 48˚

Transversal Angles Interior/Exterior Alternate interior/ alternate exterior Corresponding Same side interior/ same side exterior 75˚

Polygons A simple closed figure made of line segments A regular polygon has all sides equal in length and all angles equal in measure.

Types of Polygons 3 Triangle 9 Nonagon 4 Quadrilateral 10 Decagon 5 Pentagon 11 Undecagon 6 Hexagon 12 Dodecagon 7 Heptagon N N-gon 8 Octagon

Types of Triangles Triangles are classified according to relationships between sides: Scalene Isosceles Equilateral

Types of Triangles Triangles are also classified according to angles: Acute Equiangular Right Obtuse

Triangle Fact The measures of the interior angles of any triangle add to _____ degrees. 78˚ 40˚

Types of Quadrilaterals Parallelogram Rectangle Rhombus Square Kite Trapezoid Isosceles Trapezoid

Quadrilateral Fact The measures of the interior angles of any quadrilateral add to _____ degrees. 68˚ 65˚

Other Polygons: Angle Sum We can generalize on the sum of the measures of the interior angles of any polygon. Find the sum of the interior angles in a: dodecagon

Another Interesting Fact: The sum of the measures of the exterior angles of any polygon is always _______ degrees. Find the measure of each interior angle of a regular dodecagon

Diagonals Line segments connecting non-consecutive vertices General formula:

Three-Dimensional Shapes

Three-Dimensional Shapes 5 Platonic solids: Made completely with congruent regular polygons Tetrahedron Hexahedron Octahedron Dodecahedron Icosahedron

Three-Dimensional Shapes Drawing in 3-D “1101” Cube Prism: Rectangular and Triangular Pyramid: Square and Triangular Circular Cylinder Circular Cone Sphere

Chapter 11 Material

Metric Measurement Prefix Chart: Roots: Length ― meter (m) T G M k h dk ROOT d c m µ n p Roots: Length ― meter (m) Capacity ― liter (L) Mass ― gram (g)

Customary Measurement Length facts: 12 in. = 1 ft 3 ft = 1 yd 36 in. = 1 yd 1760 yd = 1 mi 5280 ft = 1 mi Mass facts: 16 oz = 1 lb 2000 lb = 1 T Capacity facts: 4 qt = 1 gal

Temperature Conversions

Perimeter The perimeter of any triangle (or any other type of polygon) is the sum of the measures of the lengths of its sides. 5 ft 30 m 3 ft 4 ft Assume this is a regular hexagon.

Area of a Triangle The common area formula is Find the area of each triangle. 11.5 cm 16.8 cm 12 ft 9 ft

Quadrilaterals: Area & Perimeter Square: A = P = 4b Rhombus: A = bh P = 4b Parallelogram: A = bh P = 2(a + b) Rectangle: A = bh P = 2(b + h) Trapezoid: A = P = a + b + c + d

Quadrilaterals: Area & Perimeter Find the area and perimeter of each figure. 20 ft 10 ft 8 ft 90 ft Assume this is a square. 7.65 m 5.4 m

Quadrilaterals: Area & Perimeter A rectangular field has dimensions 275 ft by 145 ft. If fence costs $1.79 per running foot, find the total cost of fencing the field. If a bag of seed costs $10.95 and covers an average of 5,000 square feet, find the total cost of seeding this field.

Area of a Regular Polygon General formula: a = length of apothem n = # of sides s = length of a side a s

Circle Circumference The distance around the circle Formulas: C = 2 π r C = π d d r r = radius, d = diameter, π = pi (a number close to 3.14159 . . .)

Circle Circumference The earth has a radius of approximately 3,960 miles. Find the distance around the earth along the equator. A bicycle tire has a diameter of 26 inches. Find how far the bike travels in 1 full revolution of the tire.

Circle Area A measure of the size of the region inside the circle Formulas: r = d ∕ 2 r d

Circle Area You measure a circle’s diameter to be 5 feet. Find the circle’s area. If the area of a circle is 250 square meters, find the radius of the circle.

The Pythagorean Theorem The sum of the squares of the lengths of the legs of a right triangle equals the square of the length of the hypotenuse. c a b

The Pythagorean Theorem Do the following represent lengths of sides of a right triangle? 6 cm, 8 cm, 10 cm 10 ft, 10 ft, 20 ft 4 mi, 5 mi, 7 mi 7 in., 24 in., 25 in.

The Pythagorean Theorem Find the missing lengths. 75 ft 11.5 cm 16.8 cm 93 yd 67 yd

Three-Dimensional Shapes

Rectangular Prism Volume: V = l w h Surface Area: A = 2 l w + 2 w h + 2 l h l = length w = width h = height h w l

Rectangular Prism Find the volume and surface area of the following room. 24 ft 8 ft 18 ft

Right Circular Cylinder Volume: a measure of space inside a 3-dimensional shape r h

Right Circular Cylinder Find the volume if r = 24 m and h = 40 m. Find the diameter of a cylindrical tank 15 ft high with a capacity of 136,000 gallons. (1 cubic foot holds approximately 7.48 gallons)

Right Circular Cylinder Surface area: Find the lateral (L) and total (T) surface areas if r = 5 feet and h = 9 feet.

Challenge! Orient an 8.5” by 11” piece of paper vertically and horizontally, folding to make a right circular cylinder. Compare volumes, lateral surface areas, and total surface areas. Which is greater ― the circumference of a tennis can lid or the height of the tennis can?

Sphere Volume: Surface Area: The earth has a radius of approximately 3,960 miles. Find the surface area and volume of the earth.

Geometry is all around us!