CPCTC – Corresponding Parts of Congruent Triangles are Download

Transcript
Geometry
Chapter 4
Key Vocabulary
Triangle – polygon with three sides
Vertex – each of the three points joining the sides of the triangle
Adjacent Sides – two sides sharing a common vertex
Right Triangle – triangle with one right angle
Legs – adjacent sides that form the right angle
Hypotenuse – side opposite the right angle
Isosceles Triangle – triangle with at least two congruent sides
Legs – the congruent sides of an isosceles triangle
Base – the third side of an isosceles triangle
Interior Angles
Exterior Angles
Congruent Triangles – when the corresponding sides and angles of each triangle are congruent
Congruence Statement – states that polygons are congruent
CPCTC – Corresponding Parts of Congruent Triangles are Congruent
Base Angles – the angles adjacent to the base
Vertex Angle – the angle opposite the base
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Geometry
Chapter 4
Postulates/ Theorems
Theorem 4.1 – Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180
Theorem 4.2 – Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum
of the measures of the two nonadjacent interior angles
Corollary to the Triangle Sum Theorem
The acute angles of a right triangle are complementary
Theorem 4.3 – Third Angles Theorem
If two angles of one triangle are congruent to two
triangles of another triangle, then the third angles
are also congruent.
Theorem 4.4 – Properties of Congruent Triangles
B
Reflexive Property of Congruent Triangles
Every triangle is congruent to itself
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E
Symmetric Property of Congruent Triangles
If ABC  DEF , then DEF  ABC
C
D
Transitive Property of Congruent Triangles
F
K
If ABC  DEF and DEF  JKL , then ABC  JKL
J
L
Postulate 19 – Side-Side-Side (SSS) Congruence Postulate
If three sides of one triangle are congruent to three sides of a
second triangle, then the two triangles are congruent
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Geometry
Chapter 4
Postulate 20 – Side-Angle-Side (SAS) Congruence Postulate
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 two triangles are congruent
Theorem 4.5 – Hypotenuse-Leg (HL) Congruence Theorem
If the hypotenuse and a leg of a right triangle are congruent to the
hypotenuse and a leg of a second right triangle, then the two triangles
are congruent
Postulate 21 – Angle-Side-Angle (ASA) Congruence Postulate
If two angles and the included side of one triangle are
congruent to two angles and the included side of another
triangle, then the two triangles are congruent
Theorem 4.6 – Angle-Angle-Side (AAS) Congruence Theorem
If two angles and the non-included side are congruent to two
angles and the non-included side of another triangle, then the
two triangles are congruent
Theorem 4.7 – Base Angle Theorem
If two sides of a triangle are congruent, then the angles opposite them are congruent
Theorem 4.8 – Converse to the Base Angle Theorem
If two angles of a triangle are congruent, then the sides opposite them are congruent
Corollary to the Base Angle Theorem
If a triangle is equilateral, then it is equiangular
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Geometry
Chapter 4
Corollary to the Converse of the Base Angle Theorem
If a triangle is equiangular, then it is equilateral
Concepts
Classification by Sides
Equilateral
Isosceles
Scalene
Classification by Angles
Acute
Right
Obtuse
Equiangular
Ways to Prove Triangle Congruent
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SSS 
SAS 
ASA 
AAS 
HL 
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