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Triangles
Chapter 4
B
What is the sum of the angles
inside a triangle?
180º?
m
4 2 5
1
A
3
C
Prove it
AC Pm
m4  m2  m5  180
1  4
m1  m4
and
and
Given
Angle Addition Postulate/Definition of a Straight
Angle
3  5
Alternate Interior Angles Theorem
m3  m5
Definition of Angle Congruence
m1 m2  m3  180
Substitution
Classifying Triangles by Sides
Equilateral - Three congruent sides
Isosceles - Two congruent sides
Scalene - No congruent sides
Classifying Triangles by Sides
Find the values of x, y, and the measures of the
sides of each triangle
4y  1
y2 6
Equilateral - Three congruent sides
3y  4
Isosceles - Two congruent sides
3x  2
x2  4
x 3
Be ready to discuss these answers in class
Classifying Triangles by Angles
Acute - All three angles < 90º
Equiangular - All three angles = 60º
Right - One right angle
Obtuse - One obtuse angle
Exterior Angle Theorem (you’ll be
proving this)
The measure of an exterior angle of a triangle is equal to the sum of
the measures of its remote interior angles
Remote Interior Angles
2
m4  m1 m2
1
3
4
Third Angle Theorem
If two angles of one triangle are congruent to two angles of another
triangle, then the third pair of angles are congruent.
P
B
Q
A
If this is true then
C
R
A  P
B  Q
C  R
Third Angle Theorem
If two angles of one triangle are congruent to two angles of another
triangle, then the third pair of angles are congruent.
P
61º
B
(9x2)º
(27x)º
Q
61º
A
C
R
Find the values of x, mC, mR, mB, and
mQ
Be ready to discuss these answers in class