#3 - Similarity, Congruence, and Proofs

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transformation

the mapping, or movement, of all the points of a figure in a plane according to a common operation

image

the new figure created from a transformation

pre-image

the original figure in a transformation

scale factor

the ratio of any two corresponding lengths of the sides of two similar figures.

congruent figures

they have the same shape and size

similar figures

they have the same shape but not necessarily the same size

dilation

transformation that changes the size of a figure, but not the shape

supplementary angles

two (or more) angles whose sum in 180 degrees

remote interior angles of a triangle

two angles non-adjacent to an exterior angle

corresponding angles

two angles that lie on the same side of the transversal in the same relative position on each parallel line.

vertical angles

two angles whose sides for opposite rays

altitude

a line segment that is perpendicular to a side of the triangle and has one endpoint at the opposite vertex

midsegment

a line segment whose endpoints are the midpoint of two sides of a triangle.

bisector

a line that divides a line segment into two line segments of equal measure, or congruent line segments.

regular polygon

a polygon that is both equilateral and equiangular

inscribed polygon

a polygon whose vertices lie on a circle

angle bisector

a ray drawn through the vertex of an angle that divides the angle into two angles of equal measure, or two congruent angles.

translation

a rigid motion that "slides" each point of a figure the same distance and direction

median

a segment connecting the vertex of a triangle to the midpoint of the opposite side

theorem

a statement that has been proven

paragraph proof

a style of proof in which the statements and reasons are presented in paragraph form

two-column proof

a style of proof in which the statements are written in the left-hand column and the reasons are written in the right-hand column.

flowchart proof

a style of proof that uses boxes and arrows to show the structure of the proof

reflection

a transformation that "flips" a figure over a line of reflection

rigid transformation

a transformation that does not change the size or the shape of a figure

rotation

a transformation that turns a figure about a fixed point though a given angle and a given direction

linear pair

adjacent supplementary angles. These angles form a straight line.

proof

an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true

proportion

an equation that states that two ratios are equal

consecutive interior angles

angle that lie on the same side of the transversal between two lines (also called 'same-side interior angles'

adjacent angles

angles in the same plane that have a common vertex and a common side, but no common interior points (side-by-side)

ratio

comparison of two quantities by division and may be written as r/s, r:s, or r to s

alternate exterior angles

exterior angles that lie on the opposite sides of the transversal

alternate interior angles

interior angles that lie on the opposite sides of the transversal

centroid

point where all medians of a triangle intersect. Also known as the "balancing point" for the triangle.

corresponding sides

sides that have the same relative position in two figures

CPCTC

Corresponding parts of congruent triangles are congruent


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