Geometry

Angles Angles describe the shape made by two straight lines that meet at a point Vertex –the point at which two lines meet Degrees are used to measure an angle Protractors are used to measure the number of degrees in an angle

Types of Angles Acute angle Right angle Obtuse Straight An angle that measures between 0 and 90 Right angle An angle that measures exactly 90 degrees Obtuse An angle that measures between 90 and 180 degrees Straight An angle that measures exactly 180 degrees

Identify the type of angle

Shapes and angles

Types of Quadrilaterals

Types of Triangles

Circles Perimeter is called Circumference Diameter Radius Pi (π) Length of the line that goes from one edge, through the center, to the other edge of a circle Radius Length of any line that goes from the center of a circle to the edge Pi (π) The ratio of the circumference to the diameter

Circle Formulas Circumference Area Pi * diameter (or pi * 2 * radius) Pi * radius * radius (pi r^2)

Other area formulas Triangle Square/Rectangle ½ base * height Square/Rectangle Length * width Don’t forget your units!!! When we calculate area, it is measured in SQUARE UNITS (sq ft, sq meters, sq in, sq cm, etc)

Test your skill Find the area and perimeter of the following 4m 0.5 m 5ft 4ft 6ft 14 cm

Stretch Break You have 3 ½ minutes

Volume Recall: area is measuring two dimensions, length and width. For volume, we measure three dimensions: length, width and height When we calculated area, we multiplied the two dimensions together. So for volume, we will multiply three dimensions together Don’t forget your units!!! When we calculate volume, it is measured in CUBIC UNITS (cu ft, cu meters, cu in, cu cm, etc)

Volume formulas Rectangular prism (a box of various shapes) L * w *h In general, area of base * height (for rectangle box l * w is area of base) We use this formula for shapes that are not so neat, like cylinders and triangular prisms (triangular boxes)

Test your skill--volume

Conversions in multiple dimensions When converting units in multiple dimensions (ie more than one, ie area and volume) we must convert for each dimension 1 cu ft = 1ft *1ft*1ft =12 in*12in*12in=______ 1cu m= 1m*1m*1m =100cm*100cm*100cm=______

Test your skill conversion 3cu ft = _____cu in 200,000 cu cm=_____cu m 512 cu ft = _____cu yards

Pythagorean Theorem a c b a^2+b^2=c^2 Used in right triangles as a relationship between sides a b c

Test your skill