# Shared Flashcard Set

## Details

Geometry - Ch. 4
Chapter 4 Vocabulary, Postulates, & Theorems
44
Mathematics
03/13/2013

Term
 4.1acute triangle
Definition
 3 acute angles
Term
 equiangular triangle
Definition
 3 congruent acute angles
Term
 obtuse triangle
Definition
 1 obtuse angle
Term
 right triangle
Definition
 1 right angle
Term
 equilateral triangle
Definition
 3 congruent sides
Term
 isosceles triangle
Definition
 scalene triangle
Term
 scalene triangle
Definition
 no congruent sides
Term
 4.2triangle sum theorem
Definition
 The sum of the measures of the angles of a triangle is 180.
Term
 auxiliary line
Definition
 an extra line or segment drawn in a figure to help analyze geometric relationships
Term
 exterior angles
Definition
 angles formed by one side of a triangle and the extension of an adjacent side
Term
 remote interior angles
Definition
 the 2 angles not adjacent to the exterior angle; each exterior angle has 2
Term
 exterior angle theorem
Definition
 The measure of an exterior angle is equal to the sum of the measures of the two remote interior angles
Term
 flow proof
Definition
 uses statements written in boxes and arrows to show the logical progression of the argument
Term
 corollary
Definition
 theorem with a proof that follows as a direct result of another theorem
Term
 corollary 4.1
Definition
 the acute angles of a right triangle are complementary
Term
 corollary 4.2
Definition
 there can be at most one right or obtuse angle in a triangle
Term
 4.3congruent
Definition
 two geometric figures that are exactly the same size and shape.
Term
 congruent polygons
Definition
 2 polygons in which all the parts of one polygon are congruent to the corresponding parts or matching parts of the other
Term
 corresponding parts
Definition
 parts of two geometric figures that are congruent
Term
 definition of congruent polygons
Definition
 two polygons are congruent if and only if their corresponding parts are congruent
Term
 third angles theorem
Definition
 if two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent
Term
 properties of triangle congruence
Definition
 Reflexive:▲ABC≅▲ABCSymmetric:If ▲ABC≅▲EFG, then ▲EFG≅▲ABC.Transitive:If ▲ABC≅▲EFG and ▲EFG≅JKL, then ▲ABC≅▲JKL.
Term
 4.4SSS Congruence
Definition
 if three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.
Term
 included angle
Definition
 the angle made by two adjacent lines is the included angle of those lines
Term
 SAS Congruence
Definition
 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.
Term
 4.5included side
Definition
 the side located between two consecutive angles of a polygon
Term
 ASA congruence
Definition
 if two angles and a third side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
Term
 AAS congruence
Definition
 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 triangles are congruent.
Term
 4.6legs of an isosceles triangle
Definition
 two congruent sides of an isosceles triangle
Term
 vertex angle
Definition
 the angle formed by the legs of an isosceles triangle
Term
 base angles
Definition
 two angles formed by the base and the two congruent sides of an isosceles triangle
Term
 isosceles triangle theorem
Definition
 if two sides of a triangle are congruent, then the angles opposite those sides are congruent
Term
 converse of isosceles triangle theorem
Definition
 if two angles of a triangle are congruent, then the sides opposite those angles are congruent.
Term
 corollary 4.3
Definition
 a triangle is equilateral if and only if it is equiangular
Term
 corollary 4.4
Definition
 each angle of an equilateral triangle measures 60
Term
 4.7transformation
Definition
 operation that remaps an original geometric figure
Term
 preimage
Definition
 the original geometric figure in a transformation
Term
 image
Definition
 new geometric figure in a transformation
Term
 congruence transformation
Definition
 one in which the image may differ from that of the preimage, but the two figures remain congruent.
Term
 isometry
Definition
 see congruence transformation
Term
 reflection
Definition
 a flip over a line called the line of reflection. each point of the preimage and image are the same distance from the line of reflection.
Term
 translation
Definition
 a slide that moves all points of the original figure the same distance in the same direction
Term
 rotation
Definition
 rurn around a fixed point called the center of rotation, through a specific angle, and in a specific direction. Each point in the preimage and image are the same distance from the center of rotation.
Term
 4.8coordinate proof
Definition
 use figures in the coordinate plane and algebra to prove geometric concepts
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