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--triangle 8 sides--octagon• 4 sides--quadrilateral 9 sides--nonagon• 5 sides--pentagon 10 sides--decagon• 6 sides--hexagon 12 sides--dodecagon• 7 sides--heptagon

QUADRILATERALSParallelogram 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 andand 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

gKing 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 39.37 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.