MII: Module 5 Geometric Figures

Angle Bisector

A ray that divides an angle into two congruent angles.

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.

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.

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.

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.

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. It maintains congruence, meaning that it preserves distance, angle measures, and parallelism.

Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

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

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. It maintains congruence, meaning that it preserves distance, angle measures, and parallelism.

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.

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. It maintains congruence, meaning that it preserves distance, angle measures, and parallelism.

Centroid of a Triangle

The point where the medians of a triangle intersect

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.

Same Side Interior Angles

The two angles that are inside (interior) the parallel lines and are on the same side of the transversal Are SUPPLEMENTARY (add up to 180 degrees)

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.

Congruence Statements

Using mathematical symbols to list corresponding pairs of congruent parts.

Altitude of a triangle

a perpendicular segment from a vertex to the line containing the opposite side

Regular Polygons

a polygon that is both equilateral and equiangular

median of a triangle

a segment from a vertex to the midpoint of the opposite side

Exterior Angles of a Triangle

an exterior angle of a triangle is equal in measure to the sum of the two non-adjacent (opposite) interior angles of the triangle.

Alternate Interior Angles

angles between 2 parallel lines and on opposite sides of a transversal

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.

Corresponding Angles

the angles that occupy the same relative position at each intersection where a straight line crosses two parallel lines. These angles are equal.