1.1Points, Lines and Planes

Undefined Terms – Words/items that are only explained using examples or descriptions.

Collinear – Points that lie on the same line.

Coplanar – Points that lie on the same plane.

Intersection – The set of points that two or more geometric figures have in common.

Space – A boundless, three-dimensional set of all points. Can contain lines and planes.

1.2 Linear Measure

Line Segment – A measurable part of a line that consists of two points, called endpoints, and all of the points between them.

Congruent Segments – Segments that have the same measure.

Constructions – A method of creating geometric figures without the benefit of measuring tools.

Generally a compass and straightedge are used.

Precision – A clustering of a group of measurements.

Depends on the smallest unit of measure available on measuring tool.

Accuracy – How close a measured value comes to the actual or desired value.

1.3 Distance and Midpoints

Distance – The length of the segment between two points.

Distance Formula

Midpoint – The point halfway between the endpoints of a segment.

Midpoint Formula

Segment Bisector – Any segment, line, or plane that intersects a segment at its midpoint.

1.4 Angle Measure

Ray – A part of a line that has one endpoint and extends indefinitely in one direction.

Opposite Rays – Two rays on the same line that share a common endpoint.

Angle – An object formed by two noncollinear rays that have a common endpoint.

Sides – The rays that make up the angle.

Vertex – The common endpoint of an angle.

Degree – The unit used to measure angles. Equal to 1/360th of a turn around a circle.

Angle Bisector – A ray that divides an angle into two congruent angles.

1.5 Angle Relationships

Perpendicular – Lines, segments, or rays that form right angles.

1.6 Two Dimensional Figures

Concave – If any of the lines that contain each side is extended and goes through the inside.

Convex – If none of the lines that contain each side is extended and never pass through the interior.

Names of Polygons

Number of Sides / Type (Name) of Polygon
3 / Triangle
4 / Quadrilateral
5 / Pentagon
6 / Hexagon
7 / Heptagon
8 / Octagon
9 / Nonagon
10 / Decagon
12 / Dodecagon
N / n-gon

Equilateral, Equiangular, and Regular

Equilateral – All sides are equal.

Equiangular – All angles are equal.

Regular – All sides and angles are equal. It would be both Equilateral and Equiangular.

Perimeter – The sum of the lengths of the sides of a polygon.

Circumference – The distance around a circle.

Area – The number of square units needed to cover a surface.

1.7 Three-Dimensional Figures

Polyhedron – A solid with all flat surfaces that enclose a single region of space.

Face – The polygons that make up the flat surface.

Edge – The line segments where the faces intersect.

Vertices – The point where three or more edges intersect.

Regular Polyhedron – A polyhedron with all faces being regular congruent polygons.

Surface Area – A two-dimensional measurement of the surface of a solid figure.

Volume – The measure of the amount of space enclosed by a solid figure.