Geometry Ch. #4 Vocabulary
Reflection
(Flip) A transformation over a line called the line of reflection. Each point of the preimage and its image are the same distance from the line of reflection
Translation
(Slide) A transformation that moves all points of the original figure the same distance in the same direction
Rotation
(Turn) A transformation around a fixed point called the center of rotation, through a specific angle, and in a specific direction, Each points of the original figure and its image are the same distance from the center
Congruence Transformation
(rigid transformation or isometry) transformation in which the position of the image may differ from that of the preimage, but the two figures remain congruent
Properties of Equilateral Triangles
-A triangle is equilateral if and only if it is equiangular -Each angle of an equilateral triangle measures 60
Proving Triangles Congruent
-SSS Congruence -SAS Congruence -ASA Congruence -AAS Congruence -HL Congruence
Auxiliary Line
An extra line or segment drawn in a figure to help analyze geometric relationships
Transformation
An operation that maps an original geometric figure onto a new figure. Can change the position, size, or shape of a figure
Vertex Angle
Angle with the sides that are the legs in an isosceles triangle
Exterior Angles of a Triangle
Angles formed by one side of the triangle and the extension of an adjacent side
Corresponding Parts
Corresponding sides and angles between two ploygons
HL Congruence
Hypotenuse-leg congruence. When two right triangles have corresponding sides that are congruent the triangles are congruent.
SSS Congruence
If three sides of one triangle are congruent to 3 sides of a second triangle then the triangles are comgruent
ASA Congruence
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the angles are congruent
AAS Congruence
If two angles and the nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent
Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent
Third Angles Theorem
If two angles of one triangle are congruent to two sides of a second triangle, then the third angles of the triangles are congruent
SAS Congruence
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent
Remote Interior Angles
Interior angles that are not adjacent to the exterior angle
Position and Label a Triangle
Make N, the vertex, on the origin Use b as the x coordinate for P Use a as the y coordinate for M
Writing a Coordinate Proof
Place a vertex on the origin and label it A. Use coordinates that are multiples of 2 because the midpoint formula involves dividing the sum of the coordinates by 2
Placing Triangles on a Coordinate Plane
Place the triangle against an axis with the origin as a vertex
Identify Missing Coordinates
Position X on the origin (0, 0) Z is on the x-axis so its coordinate is (a, 0) Y is halfway between X and Z so (a/2, b)
Coordinate Proofs
Proofs using figures in the coordinate plane and algebra to probe geometric concepts
Properties of Triangle Congruence
Reflexive, Symmetric, and Transitive Property of Triangle Congruence
Included Angle
The angle formed by two adjacent sides of a polygon
Exterior Angle Theorem
The measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles
Image
The new figure in a transformation
Preimage
The original figure in a transformation
Included Side
The side located between two consecutive angles of a polygon
Triangle Angle-Sum Theory
The sum of the angles of a triangle is 180
Base Angles
The two angles formed by the base and the congruent sides in an isosceles triangle
Legs
The two congruent sides of an isosceles triangle
Isometry
Transformation where the size does not change
Isosceles Triangle
Triangle with *at least* 2 congruent sides
Isosceles Triangle
Triangle with at least two congruent sides
Scalene Triangle
Triangle with no congruent sides
Obtuse Triangle
Triangle with one obtuse angle
Right Triangle
Triangle with one right angle
Acute Triangle
Triangle with three acute angles
Equilangular Triangle
Triangle with three congruent acute angles
Equilateral Triangle
Triangle with three congruent sides
Definition of Congruent Polygons
Two polygons are congruent if and only if their corresponding parts are congruent
Verify Congruence After a Transformation
Use the Distance formula to figure out if the distances of the corresponding segments are congruent
Congruent Polygons
When all the parts of one polygon are congruent to the cortesponding parts of the other parts
Congruent
When two geometric figures have exactly the same shape and size
