Download 3-4 Angles of a Triangle

3-4 Angles of a Triangle
• A Triangle is a figure formed by three
segments joining three noncollinear points.
• 1) Classifying triangles by their sides.
•
a) Equilateral triangle
•
– 3 congruent sides
•
b) Isosceles triangle
•
- 2 congruent sides
•
c) Scalene triangle
•
- No congruent sides
• 2) Classifying triangles by their angles.
•
a) Acute triangle
•
- has 3 Acute angles
•
b) Equiangular triangle
•
- has 3 congruent angles
•
- an Equiangular triangle is also Acute.
•
c) Right triangle
•
- has one right angle
•
d) Obtuse triangle
•
- has one obtuse angle
Theorems:
• 1) Theorem 3 - 11 Triangles Sum Theorem
•
The sum of the measures of the interior
angles of a triangle is 180°
• 2) Theorem 3 - 12 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.
B
Ex.
1
C
m<1 = m<B + m<C
Problems:
• 1) Classify the triangle
•
a)
b)
60
60
60
46
88
46
• 2) Find the value of x. Then find the measure
of the exterior angle.
x0
72
0
(2 x  11) 0
• C) Corollary – to a theorem is a statement
that can be proved easily using the theorem.
• Corollary 4 to the triangle sum theorem.
• The acute angles of a right triangle are
complementary.
C
m<A + m<C = 90°
B
A
• 3) The measure of one acute angle of a right
triangle is one-fourth the measure of the
other acute angle. Find the measure of each
acute angle.
x0
1 0
x
4
• Corollary 1
• If two angles of one triangle are  to two
angles of another triangle, then the third
angles are  .
Corollary 2
• Each angle of an equiangular triangle has a
measure of 60°
• Corollary 3
• In a triangle, there can be at most one right
angle or one obtuse angle.
• Find the values of x and y.
• 1)
2)