Download Ch 4 Triangle Congruence Notes

Ch 4 Triangle Congruence
4-1 Classifying Triangles
By Angle Measures
Acute
3 acute angles
triangle
Equiangular
triangle
3 congruent
acute angles
Right
triangle
1 right angle
Obtuse
triangle
1 angle over
90◦
By Side Length Measures
Equilateral
3 congruent
triangle
sides
Isosceles
triangle
At least 2
congruent
sides
Scalene
triangle
No congruent
sides
4-2 Angle Relationships in Triangles
Triangle
Angle-Sum
Theorem
Corollary
Corollary 42-2
Corollary 42-3
Exterior
Angle
Theorem
The sum of the measures of a triangle is
180◦
A theorem whose proof follows directly
from another theorem
The acute angles of a right triangle are
complementary
The measures of each angle in an
equiangular triangle is 60◦
The measure
of an exterior
angle of a
triangle is
equal to the
sum of the
measures of
its remote
interior angles
Third Angles If 2 angles of 1 triangle are congruent to 2
Theorem
angles of another triangle, then the 3rd
pair of angles are congruent.
4-3 Congruent Triangles
Correspondin
g angles
Correspondin
g sides
Congruent
polygons
Naming
congruent
polygons
Are in the
same
position in
polygons of
equal sides
Correspondin
g angles and
sides are
congruent
Corresponding
angles
Corresponding
sides
4-4 Triangle Congruence: SSS & SAS
SSS
If 3 sides of one
Side Side Side triangle are
Congruence congruent to the 3
sides of another
triangle, then the
triangles are
congruent.
SAS
Side Angle
Side
Congruence
If 2 sides and the
included angle of
one triangle are
congruent to the 2
sides and the
included angle of
another triangle,
then the triangles
are congruent.
4-5 Triangle Congruence: ASA, AAS, & HL
ASA
Angle
Side
Angle
Congru
ence
If 2 angles and the
included side of one
triangle are congruent to
the 2 angles and the
included side of another
triangle, then the
triangles are congruent.
AAS
Angle
Angle
Side
Congru
ence
If 2 angles and the
NONincluded side of one
triangle are congruent to
the 2 angles and the
NONincluded side of
another triangle, then
the triangles are
congruent.
Remember: they must be named in
order by corresponding parts!
HL
Hypote
nuse
Leg
Congru
ence
If the hypotenuse and leg
of a right triangle are
congruent to the
hypotenuse and leg of
another right triangle,
then the triangles are
congruent.
4-6 Triangle Congruence: CPCTC
CPCTC
Corresponding Parts of Congruent Triangles are
Congruent
Quadratic Equations
Quadratic
Equations
Factoring
ax2 + bx + c = 0
1. Take Out Something Common
2. Difference of Squares
3. Perfect Square Trinomial
4. Other – Easy
5. Other – Hard
6. Quadratic Formula
Solve
x2 + 3x – 4 = 0
x = –4, x = 1.
4-7 Introduction to Coordinate Proof
Coordinate proof Uses coordinate geometry and
algebra after positioning a figure on a
coordinate plane
Strategies for
 Use the origin as a vertex, keep
positioning
the figure in quadrant I
figures in the
 Center the figure at the origin
coordinate plane
 Center the side of a figure at the
origin
 Use one or both axes as the sides
of the figure
4-8 Isosceles & Equilateral Triangles
Legs
The
congruent
sides of an
isosceles
triangle
Vertex angle The angle included between the legs of an
isosceles triangle
Base
The side opposite the vertex angle
Base angles The 2 angles attached to the base
Isosceles
If 2 sides of a triangle are congruent, then
Triangle
the angles opposite the sides (base angles)
theorem
are congruent
Converse of If 2 angles of a triangle are congruent, then
the Isosceles the sides opposite those angles (legs) are
Triangle
congruent
theorem
Corollary 4- If a triangle is equilateral, then it is
8-3
equiangular.
Corollary 4- If a triangle is equiangular, then it is
8-4
equilateral.