Download 3-3 PPT Parallel lines and Triangle Angle Sum

Section 3-3 Parallel Lines and Triangle Angle Sum Thm
SPI 32A: identify properties of plane figures
SPI 32E: solve problems involving complementary, supplementary, congruent,
vertical, or adjacent angles
SPI 22E: apply the Triangle Angle Sum Theorem or Exterior Angle Thm to
determine measures of the angles expressed algebraically
Objectives:
• Classify triangles and find the measures of their angles
• Use exterior angles of triangles
Triangle Angle-Sum Theorem
Triangle Angle-Sum Theorem
The sum of the measures of the angles of a triangle is 180°.
mA + mB + mC = 180°
B
Interior angles
= 180
A
C
Apply the Triangle Angle-Sum Theorem
Find the value of each
variable.
Value of x
mx + 80 + 30 = 180° Triangle Angle-Sum Thm
x = 70
SPE and Simplify
Value of y
mx + m y = 180
70 + m y = 180
y = 110
Supplementary Angles
Substitution
SPE and Simplify
Value of z
mz + my + 40 = 180
mz + 110 + 40 = 180
z = 30
Triangle Angle-Sum Thm
Substitution
SPE and Simplify
Classify Triangles
Acute
All angles are acute (< 90)
Right Angle
Contains one right angle
Obtuse
Contains one obtuse angle (>90)
Classify Triangles ….. continued
Equiangular
All angles are congruent.
Equilateral
All sides are congruent.
Isosceles
At least two sides are congruent.
Scalene
NO sides are congruent.
Triangle Exterior Angle Theorem
Triangle Exterior Angle Theorem
The measure of each exterior angle of a triangle equals the
sum of the measure of its two remote interior angles.
mA = mB + mC
Using Triangle Exterior Angle Theorem
Find the value of angle 1.
By the Triangle Exterior Angle Theorem:
m1 = 63 + 60
m1 = 123
Real-world and Carpentry
Carpenters often make their own trusses for roofs of a
house. Trusses have different settings that change the
angles formed by its parts. Suppose the m2 is 32 and
m3 is 81. What will be the m1?
2
3
1
By the Triangle Exterior Angle Theorem:
m1 = 32 + 81
m1 = 113