Download RGeo Ch 4 Study Guide

Regents Geometry
Chapter 4 Study Guide
Use the following website for on-line resources (practice tests and quizzes):
http://www.glencoe.com/sec/math/geometry/geo/geo_04/
Select what you want to do and then go to Chapter 4 Congruent Triangles.
Chapter 4 – Congruent Triangles
 Definitions with images can be found using Quizlet: http://quizlet.com/24476319/flashcards
Right Angle
Acute Angle
Obtuse Angle
Acute Triangle
Obtuse Triangle
Right Triangle
Equiangular Triangle
Scalene Triangle
Isosceles Triangle
Equilateral Triangle
An angle that measures 90 degrees.
An angle that measures between 0 and 90 degrees.
An angle that measures between 90 and 180 degrees.
A triangle with three acute angles.
A triangle with one obtuse angle.
A triangle with one right angle.
A triangle with three congruent angles.
A triangle with no congruent sides.
A triangle with at least two congruent sides.
A triangle with three congruent sides.
Angle Sum Theorem The sum of the measures of the angles of a triangle is 180 degrees.
Exterior Angle
An angle formed by one side of a triangle and the extension of another side.
Remote Interior Angles
The angles of a triangle that are not adjacent to a given exterior angle.
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the
measures of the two remote interior angles.
Angle Sum Corollary - Acute The acute angles of a right triangle are complementary. That is, they
add to 90 degrees.
Angle Sum Corollary - Right & Obtuse The can be at most one right angle or one obtuse angle in a triangle.
Corresponding Parts
Congruent
Congruent Polygons
CPCTC
Third Angle Theorem
The matching sides and angles of two figures.
Two or more figures that are the same size and shape. Sides are equal in length
and angles are equal in measure.
Two polygons are congruent if and only if their corresponding parts are congruent.
Corresponding Parts of Congruent Triangles are Congruent.
If two angle of one triangle are congruent to two angles of a second triangle,
then the third angles of the triangles are congruent.
Reflexive Property
Symmetric Property
Transitive Property
∆ABC ≅ ∆ABC
Anything is equal to or congruent to itself.
If ∆ABC ≅ ∆EFG, then ∆EFG ≅ ∆ABC.
If one quantity equals or is congruent to a second quantity, then the second
quantity equals or is congruent to the first.
If ∆ABC ≅ ∆ EFG and ∆EFG ≅ ∆JKL, then ∆ABC ≅ ∆JKL.
If one quantity equals or is congruent to a second quantity, and the second
quantity equals or is congruent to a third quantity, then the first quantity equals
or is congruent to the third quantity.
SSS (Side-Side-Side) Congruence
Included Angle
SAS (Side-Angle-Side) Congruence
Included Side
ASA (Angle-Side-Angle) Congruence
AAS (Angle-Angle-Side) Congruence
HL (Hypotenuse-Leg) Congruence
Legs of an Isosceles Triangle
Vertex Angle of an Isosceles Triangle
Base Angles of an Isosceles Triangle
Isosceles Triangle Theorem
If three sides of one triangle are congruent to three sides of a
second triangle, then the triangles are congruent.
An angle that is included between two sides of a triangle.
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.
A side included between two angles.
If two angles and the included side of one triangle are
congruent to two angles and the included side of a second
triangle, then the triangles are congruent.
If two angles and the non-included side of one triangle are
congruent to the corresponding two angles and side of a second
triangle, then the two triangles are congruent.
If the hypotenuse and leg of one right triangle are congruent to
the hypotenuse and leg of another right triangle, then the right
triangles are congruent.
The two congruent sides of an isosceles triangle.
The angle formed by the legs of an isosceles triangle.
The two angles that are not the vertex angle of an isosceles triangle.
If two sides of a triangle are congruent, then the angles
opposite those sides are congruent.
Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides
opposite those angles are congruent.
Equilateral Triangle Property
A triangle is equilateral if and only if it is equiangular.
Angles of an Equilateral Triangle
Each angle of an equilateral triangle measures 60 degrees.