Download Chapter 4 Notes

Chapter 4 Notes
Classify triangles according to their sides
Equilateral
all 3 sides
are ≌
Isosceles
at least 2
sides are ≌
Scalene
no sides
are ≌
Classify triangles by their angles
Acute
Right
Obtuse
Equiangular
(3 acute ∠’s)
(1 rt. ∠)
( 1 obtuse ∠)
(all the ∠’s are =)
Right Triangle
Leg
Hypotenuse
Leg
Isosceles Triangle
Leg
Leg
Base
Interior Angles
Exterior Angles
Triangle Sum Thm – The sum of the interior
angles of a triangle is 180°
Exterior Angle Thm – The measure of an
exterior angle of a triangle is equal to the sum
of the measure of the 2 nonadjacent interior
angles.
Corollary to the Triangle Sum Thm – the acute
angles of a right triangle are complementary.
A
C
B
m∠A + m∠B = 90°
Chapter 4.2 Notes
If 2 triangles are ≌ then they have 3 corresponding sides and 3 corresponding ∠’s.
Corr. Sides
Corr. Angles
1)
1)
2)
2)
3)
3)
A
X
B
C
Y
Z
Third Angle Thm – if 2 ∠’s of one triangle are
congruent to 2 ∠’s of another triangle, then
the third angles are also congruent.
B
E
A
C
D
F
If ∠A ≌ ∠D and ∠B ≌ ∠E, then ∠C ≌ ∠F.
Chapter 4.3 Notes
Side-Side-Side Post. (SSS) – if 3 sides of one
triangle are ≌ to 3 sides of another triangle,
then the 2 triangles are congruent
≌
Side-Angle-Side Post. (SAS) – if 2 sides and the
included ∠ of one triangle are ≌ to 2 side
and the included angle of a second triangle,
then the 2 triangles are ≌.
≌
Chapter 4.4 Notes
Angle-Side-Angle Post. (ASA) – if 2 ∠’s and the
included side of one triangle are ≌ to 2 ∠’s and the
included side of a second triangle, then the 2
triangles are congruent
≌
Angle-Angle-Side Post. (AAS) – if 2 ∠’s and a
nonincluded side of one triangle are ≌ to 2 ∠’s
and the corresponding nonincluded side of a
second triangle, then the 2 triangles are ≌.
≌
Chapter 4.5 Notes
Once you have 2 triangles ≌ then you can
say anything you want about their
corresponding parts.
(It is called Corresponding Parts of
Congruent Triangles are Congruent)
*You can use the acronym C.P.C.T.C
Chapter 4.6
Base Angle Thm – if 2 sides of a triangle are ≌, then
the angles opposite them are ≌.
If
then
If AB ≌ AC, the ∠B ≌ ∠C
Converse of the Base Angles Thm – If 2 ∠’s of a
triangle are ≌, then the sides opposite them are
≌.
If
then
Corollaries
If a triangle is equilateral, then it is equiangular.
If
then
If a triangle is equiangular, then it is equilateral.
If
then
Hypotenuse-Leg Congruence Thm (HL)
If the hypotenuse and a leg of a right triangle
are ≌ to the hypotenuse and a leg of a
second right triangle, then the 2 triangles
are ≌.
A
D
B
C
E
If BC ≌ EF and AC ≌ DF, then
F
ABC ≌
DEF
Chapter 4.7 Notes
Coordinate Proof – involves placing geometric
figures in a coordinate plane. Then you can
use the Distance Formula and the Midpoint
Formula, as well as postulates and theorems,
to prove statements about the figures.