Draft MII: Module 5 Geometric Figures

Equilateral Triangle

A Regular Polygon with 3 equal sides (Equilateral) and 3 equal angles (Equiangular). Each angle measures exactly 60°.

Vertex

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

Angle

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

Perpendicular Bisector

A special kind of Segment, Ray or Line that intersects a given segment at a 90° angle, and passes through the given segments MidPoint.

Isosceles Trapezoid

A special type of quadrilateral with one pair of opposite parallel sides that are NOT equal in length. A pair of opposite sides that are congruent but NOT parallel. The base angles are congruent to each other. Its diagonals are congruent.

Parallelogram

A special type of quadrilateral with two pairs of opposite sides that are congruent and parallel. Adjacent sides are different in length. Opposite angles are congruent. Its diagonals bisect each other but are not congruent.

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.

Transformation

An operation that maps an original figure (pre-image) onto a new figure (image) marked by Prime Notation. The shape may or may not, still have the same size, area, angles and line lengths.

Rigid motions

Any transformation that maintains the congruence of a shape. Meaning that it preserves distance, angle measures, and parallelism within a shape.

Included

Between two other sides or angles

Reflection

FLIP; A Rigid-Motion Transformation that moves points across a line of reflection. The segment connecting corresponding pre-image and image points is bisected perpendicularly by the line of reflection.

Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

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

Perpendicular Lines

Lines that intersect at 90°. The slopes of the lines are opposite reciprocals. For example: Horizontal and Vertical grid lines on the coordinate plane. Or: m = -1/2 & m = 2/1

Angle of Rotation

Refers to the number of degrees a figure has been rotated around a fixed point, with a counterclockwise rotation being considered a positive direction of rotation.

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.

Conjecture

a mathematical statement that has not yet been proven.

Line

an object with no thickness that extends infinitely in two directions

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.

Sequence of transformations

A combination of two or more transformations, each performed on the previous image. Some combinations of transformations are commutative and will result in the same final image.

Line of symmetry

A line that reflects a figure onto itself. It divides a figure into two mirror-image halves with corresponding congruent sides and angles.

Midpoint of a Segment

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

Angle Bisector

A ray that divides an angle into two congruent angles.

Square

A special type of quadrilateral that is also considered a parallelogram, a rectangle, and a rhombus. Opposite sides are parallel and congruent. Adjacent sides are perpendicular and congruent, making all 4 sides equal in length. Its diagonals are perpendicular, congruent and bisect each other. Its diagonals also bisect the angles.

Quadrilateral

A two-dimensional closed shape which has four straight sides and four corners. It is the parent of a whole family of figures, each with their own distinct names and characteristics.

Polygon

Any two-dimensional closed shaped with straight line segments as sides. Polygons that are considered "Regular" have congruent sides and congruent angles. The name tells you how many sides the shape has.

Rectangle

Opposite sides are parallel and congruent to each other meaning that is a special type of parallelogram, which also has adjacent sides that are perpendicular but different in length. Its diagonals are congruent and bisect each other.

Rhombus

Opposite sides are parallel and congruent to each other meaning that is a special type of parallelogram. Adjacent sides are also congruent, making all 4 sides equal in length. Opposite angles are congruent. Its diagonals are perpendicular and bisect each other. Its diagonals also bisect the angles.

Translation

SLIDE; A Rigid-Motion Transformation that moves points the same distance and direction along lines that are parallel to each other.

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.

Rotation

TURN; A Rigid-Motion transformation that moves points along a circular arc with a specified center and angle. The segments connecting pre-image and image points to the center of rotation are equal in length.

Endpoint

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

Circle

The set of all points in a plane that are equidistant from a fixed point called the center of the circle. There are a total of 360° in a full circle.

Diagonal

These are formed when opposite vertices of a polygon are connected by a line segment, which are not already joined by an edge.

Congruent shapes

These have the same size and the same shape. When shapes are congruent, all corresponding sides and angles are also congruent.

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.

Rotational symmetry

When a figure can be carried onto itself through rotation about its center. The angle of rotation is equal to 360 divided by the number of times you can rotate that shape to match up to itself.

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.

Pythagorean Theorem

a²+b²=c²; An equation for Right Triangles that relates the side lengths to each other. a and b are the legs that join at the 90° angle. c is the Hypotenuse, the longest side, that is opposite from the 90° angle.

Consecutive

following in order immediately after another.

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.

Coincide

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