Unit 2: Transformations, Triangles, and Quadrilaterals

Point of Currency

when three of more lines intersect at one point, the lines are said to be concurrent. The point where the three or more lines intersect is called this.

Composition of Transformations

where two or more transformations are performed.

Kite

quadrilateral with exactly two distinct pairs of congruent consecutive sides.

Triangle Congruence Criteria

SSS, SAS, ASA, and AAS.

Transformation

a change in the position, size, or shape of a figure.

Circumscribed Circle

a circle that contains all the vertices of a polygon.

Auxiliary Line

a line that can be added to a figure to help complete the proof.

Rhombus

a parallelogram with four congruent sides.

Rectangle

a parallelogram with four right angles.

Parallelogram

a quadrilateral with both pairs of opposite sides parallel.

Altitude of a Triangle

a segment from a vertex of the triangle, perpendicular to the opposite side of the triangle.

Corollary

a statement that results directly from a theorem.

Rigid Motion

a transformation that preserves size and shape.

Remote Interior Angle

an interior angle that is not adjacent to a given exterior angle.

Indirect Proof

can be used when the conclusion is a negative statement.

Exterior Angle

formed by one side of a triangle.

Interior Angle

formed by two sides of a triangle.

Rotational Symmetry

if a figure is constructed by a reflection.

Isosceles Triangle Theorem

if a triangle is isosceles, then the base angles are congruent.

Translation

is a rigid motion in which every point is moved the same distance and in the same direction.

Flowchart Proof

one way to organize your thoughts into a logical sequence.

Corresponding Parts

results from one-to-one matching of sides and angles from one figure to another.

Reflection

sometimes called "flips" because it flips like a pancake.

Incenter

the angle bisectors of the angles of a triangle are concurrent, and this point of concurrency is called this.

Directed Line Segment

the distance and direction of the translation.

Image

the figure after the transformation.

Inscribed Circle

the largest possible circle that can be drawn on the inside of a plane figure.

Line of Reflection

the line that the reflection maps to itself.

Exterior Angle Theorem

the measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

Pre-image

the original figure.

Circumcenter

the perpendicular bisectors of the sides of a triangle are concurrent. The point of concurrency is called this.

Orthocenter

the point of currency of the altitudes of a triangle.

Centroid

the point of currency of the medians of a triangle.

Median

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

Midsegment

the segment whose endpoints are the midpoints of two sides of a triangle.

Median of a Trapezoid

the segment with endpoints at the midpoint of each leg of the trapezoid.

Angle of Rotational Symmetry

the smallest angle of rotation.

Triangle Sum Theorem

the sum of the measures of the angles of a triangle is 180 degrees.

Rotation

the transformation that maps P to P' across line l such that *if P is not on l, then l is a perpendicular bisector or PP' and *if P is on l, then P=P'.

Congruent

two figures are congruent if and only if a composition of rigid motions maps one to the other.