Triangle Sum Properties
Classify triangles and find measures of their angles.
Standard:MG 2.3
Draw triangles from given information about them.
Student Objective:
-- Students will draw triangles and solve
triangle sum problems from given
information about them by using equations
and scoring an 80% proficiency on an exit
slip.
A triangle is a polygon with three sides.
A triangle with vertices A, B, and C is called
“triangle ABC” or “∆ABC.”
A
B
C
Classifying Triangles by Sides
A scalene triangle is a triangle with no congruent sides.
An isosceles triangle is a triangle with at least two
congruent sides.
An equilateral triangle is a triangle with three
congruent sides.
Classifying Triangles by Angles
• An acute triangle is a triangle with three acute
angles.
• A right triangle is a triangle with one right
angle.
• An obtuse triangle is a triangle with one
obtuse angle.
• An equiangular triangle is a triangle with
three congruent angles.
Classification By Sides
Classification By Angles
Triangle Sum Theorem
The sum of the measures of the interior
angles of a triangle is 180o.
1
3
2
m<1 + m<2 + m<3 = 180°
Property of triangles
The sum of all the angles
equals 180º degrees.
60º
90º
+
30º
180º
60º
90º
30º
Property of triangles
The sum of all the angles
equals 180º degrees.
40º
50º
90º
40º
90º
+
50º
180º
Property of triangles
The sum of all the angles
equals 180º degrees.
60º
60º
+
60º
180º
60º
60º
60º
Ex: 1What is the missing angle?
70º
70º
+ x
180º
x
70º
70º
180 – 140 = 40˚
EX: 2 What is the missing
angle?
x
30º
90º
90º
30º
+
x
180º
180 – 120 = 60˚
Ex: 3What is the missing angle?
x
60º
60º
60º
60º
+
x
180º
180 – 120 = 60˚
EX 4:
What is the missing angle?
X
78º
30º
180 – 108 = 72˚
30º
78º
+
X
180º
What is the missing angle?
?
40º
40º
180 – 80 = 100˚
40º
40º
+
?
180º
Find all the angle measures
35x
45x
180 = 35x + 45x + 10x
180 = 90x
2=x
10x
90°, 70°, 20°
DAY 2: Triangle Sum Theorem
Continued
Standard : MG 2.2 Use the properties of
complementary and supplementary angles
and the sum of angles of a triangle to solve
problems involving an unknown angle.
Student Objective (s):
-- Students will use properties of the sum
of triangles and solve problems with an
unknown angle from given information
about them by using equations and scoring
an 80% proficiency on an exit slip.
What can we find out?
The ladder is leaning
on the ground at a
65º angle. At what
angle is the top of
the ladder touching
the building?
180 = 65 + 90 + x
180 = 155 + x
25˚ = x
65°
Extention to Triangle Sum Theorem
The acute angles of a right triangle are
complementary.
m∠A + m∠B = 90o
Find the missing angles.
The tiled staircase shown below forms a right triangle.
The measure of one acute angle in the triangle is twice the
measure of the other angle.
Find the measure of each acute angle.
Con’
Find the missing angles.
SOLUTION:
2x + x = 90
3x = 90
x = 30˚
2x = 60˚
Find the missing angles.
2x + (x – 6) = 90˚
3x – 6 = 90
3x = 96
x = 32
2x = 2(32) = 64˚
(x – 6) = 32 – 6 = 26˚
Class work
Read Lesson 4.1 “Triangle Sum” in
your textbook and review the
Power Point lesson again.
Homework
In your textbook:
Lesson 4.1/ 1-9, 17, 25