GEOMETRY REVIEW Grades 5 - 8

Point– a location in space. Line-- a straight path that goes on forever in both directions. Line segment– a straight path between 2 points, called its endpoints. A B

Ray– a straight path that goes on forever in one direction from an endpoint. Angle– two rays of line segments with a common endpoint, called the vertex.

Types of lines Parallel lines—lines that never meet and are the same distance apart. Intersecting lines– lines that meet.

Types of Angles Acute angle measures between 0 and 90 degrees. Obtuse angle measures between 90 and 180 degrees.

Types of Angles Right angle measures 90 degrees. Straight angle measures 180 degrees.

POLYGONS A polygon is a flat 2-dimensional figure made up of 3 or more line segments called sides. The sides of a polygon are connected end-to- end and make a closed figure. Each endpoint where two sides meet is called a vertex. The plural of vertex is vertices.

REGULAR POLYGONS A regular polygon is a polygon whose sides all have the same length and whose angles are all the same size. We say that a regular polygon is both equilateral and equiangular.

NAMES OF POLYGONS Polygons are named according to the number of sides. 3 sides--triangle8 sides--octagon 4 sides--quadrilateral9 sides--nonagon 5 sides--pentagon 10 sides--decagon 6 sides--hexagon 12 sides--dodecagon 7 sides--heptagon

QUADRILATERALS Parallelogram Trapezoid (2 pair of parallel sides) (1 pair of parallel sides) (opposite sides are congruent) (diagonals bisect each other) (opposite angles are congruent) Rectangle Rhombus (properties of parallelogram (properties of parallelogram and and has 4 right angles) has all sides are congruent) (diagonals are congruent (diagonals are perpendicular) Square (properties of parallelogram, has 4 right angles, all sides are congruent) (diagonals are congruent, diagonals are perpendicular)

GEOMETRIC SOLIDS … are 3-dimensional figures. The flat surfaces of the solid are called faces. The faces of the solid meet to form line segments called edges. The corners of a solid are called vertices. EDGES = Faces + Vertices - 2

POLYHEDRONS A polyhedron is a geometric solid whose surfaces are formed by polygons. The faces of a polyhedron are all polygons. A polyhedron does not have any curved surfaces. A polyhedron is regular if all of its faces are the same size and shape.

REGULAR POLYHEDRONS Tetrahedron…has 4 faces of equilateral triangles (also called a pyramid) Cube…has 6 faces of squares (also called prism) Octahedron…has 8 faces of equilateral triangles Dodecahedron…has 12 faces of regular pentagons Icosahedron…has 20 faces of equilateral triangles

AREA Area is the amount of surface inside a shape. Area is measured in square units such as square inches or square centimeters. Area of a parallelogram = base x height Area of a rectangle = base x height or length x width Area of a triangle = base x height 2 Area of a circle = 3.14 x radius x radius

PERIMETER …..is the distance around a shape. The perimeter is the sum of all the sides. 4 cm 3 cm 3 cm Perimeter = 4 cm + 3 cm + 4 cm + 3cm 4 cm Perimeter = 14 cm

METRIC PREFIXES Kilo Hecto Deca m Deci Centi Milli l g King Henry Died……… Drinking Chocolate Milk. To change from one measure to another, simply move the decimal point to the right or left.

METRIC MEASURES For length use meters, etc. For weight (mass) use grams, etc. For volume use liters, etc.

Metric Measures A meter is slightly longer than one yard. 1 meter is about inches 1 inch is about 2.5 centimeters 1 kilometer is about 0.6 mile 1 mile is about 1.6 kilometers A liter is slightly more than one quart. 1 liter is about 1.1 quarts A gram is about the weight of one paper clip. 1kilogram is about 2.2 pounds.