Module 1: Reasoning with Shapes
Composite Figure
A figure that is formed by combining different shapes.
Distance Formula
A formula that states that if (x₁ , y₁) and (x₂, y₂) are two points on the coordinate plane, then the distance d between them is given by d = √[( x₂ - x₁)² + (y₂ - y₁)²]
Midpoint Formula
A formula that states that if (x₁ , y₁) and (x₂, y₂) are two points on the coordinate plane, then the midpoint of the line segment that joins these two points is (x₁+x₂)/2, (y₁+y₂)/2
Auxiliary Line
A line or line segment added to a diagram to help in solving or proving a concept.
Diagonal
A line segment joining two vertices of a polygon but is not a side of the polygon.
Perpendicular Bisector
A line, line segment, or ray that bisects a line segment and is also perpendicular to the line segment.
Segment Bisector
A line, line segment, or ray that divides a line segment into two line segments of equal length.
Conjecture
A mathematical statement that appears to be true, but has not been formally proved.
Line segment
A part of a line between two points on the line, called the endpoints. A distance along a line is the length of a _________________________________ connecting two points on the line.
Straightedge
A ruler with no numbers
Rigid Motion
A special type of transformation that preserves the size and shape of the figure.
Line
A straight, continuous arrangement of an infinite number of points; that has an infinite length, but no width.
Compass
A tool used to create arcs and circles.
Translation
A type of rigid motion transformation that "slides" a figure up, down, left, or right.
Reflection
A type of rigid motion transformation that. "flips" a figure across a line.
Rotation
A type of rigid motion transformation that. "spins" a figure about a point.
Construct
The creation of exact figures without measurements, using paper folding or a compass and a straightedge.
Midpoint
The point that divides the line segment into two congruent segments.
Slope
The steepness and direction of a line.
Adjacent
When sides share a vertex.
Sketch
When you create a geometric figure without tools. Accuracy is not important.
Draw
You can use tools such as rulers, protractors, or a coordinate plane to create geometric figures with exact lengths and areas.
Transformation
Mapping, or movement, of the points of a figure on a plane according to a common action or operation.
Point
Described simply as a location. In geometry it has no size or shape, but it is often represented using a dot. In a diagram, it can be labeled using a capital letter.