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