Topic 1: Basics of Geometry
Definitions:
Point - has location only, no size, no height, no depth. Use CAPITAL letters to name.
Line- a straight, unbroken set of points that goes on forever, infinite length, not thickness.
Line Segment - a line that has two endpoints
Plane - a surface that has length and width, but no thickness. A flat surface that extends forever (Name using 3 collinear points)
Ray - A line that contains only one end point. It goes on forever in one direction. (name the endpoint first)
Opposite Rays - Two rays that share a common endpoint and extend in opposite directions.
Collinear - Points that lie on the same line.
Coplanar - Points that lie on the same plane
Angle - Two rays that share a common endpoint, provided the two rays do not lie on the same line. The common endpoint is the vertex.
Video Examples:
Points, Lines, Planes
Point - has location only, no size, no height, no depth. Use CAPITAL letters to name.
Line- a straight, unbroken set of points that goes on forever, infinite length, not thickness.
Line Segment - a line that has two endpoints
Plane - a surface that has length and width, but no thickness. A flat surface that extends forever (Name using 3 collinear points)
Ray - A line that contains only one end point. It goes on forever in one direction. (name the endpoint first)
Opposite Rays - Two rays that share a common endpoint and extend in opposite directions.
Collinear - Points that lie on the same line.
Coplanar - Points that lie on the same plane
Angle - Two rays that share a common endpoint, provided the two rays do not lie on the same line. The common endpoint is the vertex.
Video Examples:
Points, Lines, Planes
Rays
Opposite Rays
Collinear and Coplanar
Naming Angles
Topic 2: Segments and Congruence
Definitions:
Congruent - same size/measure. Lines, angles, and shapes can be congruent.
Segment Addition Postulate - If B is between A and C, then AB + BC = AB (the adjacent pieces add to equal the whole segment)
Bisect - split into two equal parts; "cut in half"
Helpful Hints:
Congruent - same size/measure. Lines, angles, and shapes can be congruent.
Segment Addition Postulate - If B is between A and C, then AB + BC = AB (the adjacent pieces add to equal the whole segment)
Bisect - split into two equal parts; "cut in half"
Helpful Hints:
Video Examples:
Segment Addition
Segment Addition
Topic 3: Midpoint and Distance Formula
Definitions:
Midpoint - The point that divides a segment into two equal lengths; "the middle of the points".
Distance - The length between two points.
Helpful Hints: see formulas below
Midpoint - The point that divides a segment into two equal lengths; "the middle of the points".
Distance - The length between two points.
Helpful Hints: see formulas below
Video Examples:
Distance and Midpoint Formula
Topic 4: Measure and Classify Angles
Definitions:
Acute - An angle whose measure is between 0 and 90 degrees.
Right - An angle whose measure is exactly 90 degrees.
Obtuse - An angle whose measure is between 90 and 180 degrees.
Straight - An angle whose measure is exactly 180 degrees.
Helpful Hints:
Acute - An angle whose measure is between 0 and 90 degrees.
Right - An angle whose measure is exactly 90 degrees.
Obtuse - An angle whose measure is between 90 and 180 degrees.
Straight - An angle whose measure is exactly 180 degrees.
Helpful Hints:
Video Examples:
Measure and Classify Angles
Measure and Classify Angles
Topic 5: Describe Angle Pair Relationships
Definitions:
Adjacent - Two angles that share a ray and have a common vertex; next to each other.
Complementary - Two angles whose sum is 90 degrees.
Supplementary - Two angles whose sum is 180 degrees.
Linear Pair - Two adjacent angles that make a line. They are supplementary.
Vertical - Two non-adjacent angles formed by the intersection of two lines. They are congruent. They often look like an "X".
Helpful Hints: see images below
Adjacent - Two angles that share a ray and have a common vertex; next to each other.
Complementary - Two angles whose sum is 90 degrees.
Supplementary - Two angles whose sum is 180 degrees.
Linear Pair - Two adjacent angles that make a line. They are supplementary.
Vertical - Two non-adjacent angles formed by the intersection of two lines. They are congruent. They often look like an "X".
Helpful Hints: see images below
Video Examples:
Describe Angle Pairs Relationships
Describe Angle Pairs Relationships
Topic 6: Classifying Polygons
Definitions:
Polygon - A closed figure with at least 3 line segments called sides (no curved edges) AND each side intersects exactly 2 other sides at vertices.
Convex - A polygon in which none of the sides go into the interior of the polygon.
Concave - A polygon in which some of the sides "cave in" towards the interior of the polygon.
Equilateral - All sides are congruent.
Equiangular - All angles are congruent.
Regular Polygon - A convex polygon that is both equilateral AND equiangular.
Helpful Hints:
Polygon - A closed figure with at least 3 line segments called sides (no curved edges) AND each side intersects exactly 2 other sides at vertices.
Convex - A polygon in which none of the sides go into the interior of the polygon.
Concave - A polygon in which some of the sides "cave in" towards the interior of the polygon.
Equilateral - All sides are congruent.
Equiangular - All angles are congruent.
Regular Polygon - A convex polygon that is both equilateral AND equiangular.
Helpful Hints:
Video Examples:
Classifying Polygons
Classifying Polygons
Topic 7: Find Area, Circumference, and Perimeter
Definitions:
Perimeter - The distance around a figure. Add all of the sides. Measured in units of length (m, in, ft, etc...)
Circumference - The distance around a circle. C=(pi)d = 2(pi)r Measured in units of length (m, in, ft, etc...)
Area - The amount of surface covered by a figure. Measured in square units (m^2, in^2, ft^2, etc..). The formulas are listed below:
Helpful Hints:
The base and height are always perpendicular to each other.
Perimeter - The distance around a figure. Add all of the sides. Measured in units of length (m, in, ft, etc...)
Circumference - The distance around a circle. C=(pi)d = 2(pi)r Measured in units of length (m, in, ft, etc...)
Area - The amount of surface covered by a figure. Measured in square units (m^2, in^2, ft^2, etc..). The formulas are listed below:
- Square: A = s^2, where s is the side length.
- Rectangle: A = l*w or A =b*h, where l is length, w is width, b is base, and h is height.
- Triangle: A = .5b*h or A = b*h/2, where b is the base and h is the height. It's half of a rectangle.
- Circle: A = pi*r^2
Helpful Hints:
The base and height are always perpendicular to each other.
Video Examples:
Area, Perimeter, Circumference
Area, Perimeter, Circumference