Download Notes Sec. 4.1 - Little Miami Schools

Section 4.1: Triangle Classification (Review)
Classifying Triangles
By Sides:
• Scalene ­ no congruent sides
• Isosceles ­ at least 2 congruent sides
• Equilateral ­ 3 congruent sides
Classifying Triangles
By Angles:
•
Acute ­ 3 acute angles
•
Right ­ 1 right angle
•
Obtuse ­ 1 obtuse angle
•
Equiangular ­ 3 congruent angles
Hypotenuse:
the opposite side of the right angle
Legs:the sides that form the right angle of a right triangle
­­the congruent sides of an isosceles triangle­­
leg
hypotenuse
leg
leg
leg
base
In an isosceles triangle, we
refer to the base and the legs.
base angles are also congruent
Base Angles Theorem:
If 2 sides of a triangle are congruent, then the angles opposite them are congruent.
Converse of Base Angles Theorem:
If ...
Triangle Sum Theorem: sum of measures of the interior angles of a triangle is 180O.
Exterior Angle Theorem: the measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 non­adjacent interior angles
Exterior Angles Fact:
0
­ the sum of the exterior angles of a triangle is 360
Exterior Angles
An exterior angle forms a linear pair with its adjacent interior angle, so they sum to what?
Interior Anlges
Prove the Triangle Sum Theorem:
B
2
Given: ΔABC
Prove: m<1 + m<2 + m<3 = 180
A
3
1
Corollary to the Triangle Sum Theorem:
The acute angles of a right triangle are complementary.
A
m<A + m<B = 90 o
B
Ex. Solve for x.
3x0
(2x ­ 15)0
C
Examples: Solve for x.
b)
a)
(5x + 4)0
(4x ­8)0
360
420
77
0
c)
x0
2x0
(4x + 8)0
d) An equilateral triangle has 1 angle measure of 4x0. What is the value of x?
e) In triangle ABC, m<A=42. The measure of <B is 8 less than twice m<A. What is the measure of the exterior angle at vertex C?