#3 - Similarity, Congruence, and Proofs
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
