Download By angles - Lisle CUSD 202

Triangles and Angles
Sec 4.1
GOALS:
To classify triangles by their angles
and sides
To find missing angle measures in
triangles
Triangle
Triangle – formed by three line segments that Vertex B
B
intersect only at their endpoints.
Sides AB & CB are adjacent to vertex B
C
A
Side AC is opposite angle B
The line segments are AB , BC , and AC
angle
ABC
Angle and Side Classifications

Triangles can be classified by their sides and angles.

By sides

Scalene - no congruent sides

Equilateral - three congruent sides

Isosceles - at least two congruent sides
Angle and Side Classifications

Triangles can be classified by their sides and angles.

By angles

Acute – an acute triangle is acute because it has three acute angles

Obtuse – an obtuse triangle is obtuse because it has one obtuse angle

Right – a right triangle is right because it has one right angle

Equiangular – an equiangular triangle has three congruent sides
Lets classify some triangles
Notice: All triangles have at least two acute angles so they are
classified by the measure of the third angle.
Special triangles
Right Triangle
Leg
“a”
Hypotenuse
“c”
Isosceles Triangle
Leg
Leg
“b”
Can you have an isosceles right triangle?
(the base would be the hypotenuse)
Leg
base
Triangle Sum Theorem

The sum of the measures of the angles in a triangle is 180
degrees
x
y
mx  my  mz  180
z
If x = 55, and y = 75,
then z = 180 – (55+75) = 50
Exterior Angles of a Triangle

Exterior angles are angles that are adjacent to the interior
angles in a triangle. There are 6 in total, 3 pairs of congruent
angles.
x
y

z
It is customary to only talk about one exterior angle at each
vertex.
v
x
mx  mv  180
Exterior Angles Theorem

The measure of an exterior angle is equal to the sum of the two
remote interior angles.
x
y

m1  mx  my
1
If x = 35 degrees and y = 45 degrees, then the measure of
angle 1 is equal to 80.
Corollary

A corollary to a theorem is a statement that can be proved
easily using a theorem.
Corollary to the Triangle Sum Theorem
The acute angles of a right triangle are complementary.
mx  my  90
y
x
You Try! Find the missing angle
measure and classify each triangle
z
45
30
25
y
40
x
a
40
55
55
Examples
Find x or y.

2y
(4 x  5)
(3x  11)
50
x
40
75