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Triangles
Chapter 4
B
What is the sum of the
angles inside a triangle?
180º?
m
4 2 5
A
1
3
C
Prove it
AC m
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
C
R
∠A ≅ ∠P
∠B ≅ ∠Q
If this is true then ∠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
A
61º
(27x)º
C
Q
R
Find the values of x, m ∠C , m ∠R , m ∠B , and m ∠Q
Be ready to discuss these answers in class