Download Corollary to the Triangle Sum Theorem

Geometry Section 4.1
Triangle Sum Theorem
A triangle is the figure formed by
three line segments joining three
noncollinear points.
A
B
ABC
C
Goals for today’s class:
1. Classify triangles according to their angles and
sides.
2. Know and apply the Triangle Sum Theorem.
3. Know and apply the Exterior Angle Theorem.
4. Identify new vocabulary terms.
Triangles are classified according to their angles and sides.
Angle classification:
equiangular
3 congruent angles
acute
3 acute angles
right
1 right angle
obtuse
1 obtuse angle
Side classification:
equilateral
3 congruent sides
isosceles
2 congruent sides
scalene
0 congruent sides
Examples: Classify each triangle
according to its angles and sides.
right isosceles
acute scalene
Theorem 4.1: Triangle Sum Theorem
The sum of the measures of180
the
three angles of a triangle is ____.
(Proof on p.196 of the text)
Examples: Find the value of x.
35  118  x  180
153  x  180
x  27
Examples: Find the value of x.
180  65  71  44
180  44  136
Examples: Find the value of x.
90  x  16  x  180
x  16  x  90
2 x  106
x  53
The angle of x° in example b) is called
an exterior angle of the triangle. An
exterior angle of a triangle is formed
by extending a side
of the triangle.
Note that the exterior angle will form a
_________with
an interior angle of
linear pair
the triangle.
In example b) we found x to equal
136. Note that ____________.
65  71  136
This work leads us to the following
theorem.
Theorem 3.5.3 Exterior Angle Theorem
The measure of an exterior angle
of a triangle is equal to the sum of
the two remote interior angles.
For the triangle to the right,
m1  m2  m3
Example: Find the value of x.
2 x  10  x  65
x  55
A corollary is a statement easily
proven using a particular theorem.
Example c) on the previous page
illustrates the following corollary:
90  x  16  x  180
x  16  x  90
Corollary to the Triangle Sum
Theorem
The acute angles of a right triangle
are complementary
_____________.