Module 7: Constructions & Congruence

Midpoint of a Segment

A point on a line segment, exactly in the middle, that divides it into two congruent parts.

Vertex

A point where two or more line segments meet. A corner.

Angle Bisector

A ray that divides an angle into two congruent angles.

Angle

A shape, formed by two rays that share a common point (the vertex).

Isosceles Triangle

A triangle that has two sides with equal length and two angles with equal measure.

Equilateral Triangle

A triangle with three equal sides and three equal angles.

Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

In congruent figures, the corresponding angles have equal measures and the corresponding sides have equal measures.

Side-Side-Side Postulate (SSS)

States that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.

Side-Angle-Side Postulate (SAS)

States that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

Angle-Side-Angle Postulate (ASA)

States that triangles are congruent if any two angles and their included side are equal in both triangles.

Endpoint

The point at either end of a segment or arc, or the first point of a ray.

Circumscribed About

To Draw a figure AROUND another, touching it at points but not crossing it. A Circle must share the same Center and pass through all the Vertices of a Polygon to Circumscribe it.

Inscribed In

To Draw a figure INSIDE another, so that their boundaries touch but do not intersect. A Polygon must share the same Center and the distance from the Center to any Vertex must be equal to the Radius of the Circle, in order to be Inscribed in it.

Congruence Statements

Using mathematical symbols to list corresponding pairs of congruent parts.

Geometric Constructions

a geometric drawing that uses a limited set of tools, usually a compass and straight edge. They are based on properties of geometric figures and the definitions of the rigid-motion transformations.

Conjecture

a mathematical statement that has not yet been proven.

Line

an object with no thickness that extends infinitely in two directions

Congruent

meaning to have the exact same measurements and dimensions.

Corresponding

occupy the same relative position refers to parts that match, or that occupy the same Relative position.

Ray

part of a line consisting of one endpoint and extending infinitely in one direction

Line Segment

part of a line that has two endpoints and all the points between them.

Coincide

when two points or line segments occupy the same position on the plane.