Triangle Sum Properties

1
Triangle Sum Properties

• Classify triangles and find measures of their
  angles.

StandardMG 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.
2

• A triangle is a polygon with three sides.
• A triangle with vertices A, B, and C is called
  triangle ABC or ?ABC.

A
C
B
3

• 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.

4

• 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.

5
Classification By Sides
Classification By Angles
6
Triangle Sum Theorem

• The sum of the measures of the interior angles of
  a triangle is 180o.

mlt1 mlt2 mlt3 180
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Property of triangles

• The sum of all the angles
• equals 180º degrees.

60º
90º
30º

60º
180º
30º
90º
8
Property of triangles

• The sum of all the angles
• equals 180º degrees.

40º
90º
40º
50º

180º
50º
90º
9
Property of triangles

• The sum of all the angles
• equals 180º degrees.

60º
60º
60º
60º

180º
60º
60º
10
Ex 1What is the missing angle?
70º
70º
x
x

180º
70º
70º
180 140 40
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EX 2 What is the missing angle?
90º
x
30º
x

180º
90º
30º
180 120 60
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Ex 3What is the missing angle?
x
60º
60º
x

60º
60º
180º
180 120 60
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EX 4What is the missing angle?
X
30º
78º
X

78º
30º
180º
180 108 72
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What is the missing angle?
?
40º
40º
?

40º
40º
180º
180 80 100
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Find all the angle measures
180 35x 45x 10x
180 90x
2 x
90, 70, 20
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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.
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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
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Extention to Triangle Sum Theorem
The acute angles of a right triangle are
complementary.
m?A m?B 90o
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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.

Cont
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Find the missing angles.
SOLUTION
2x x 90
3x 90
x 30
2x 60
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Find the missing angles.
2x (x 6) 90
2x 2(32) 64
3x 6 90
3x 96
(x 6) 32 6 26
x 32
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Class work

• Read Lesson 4.1 Triangle Sum in your textbook
  and review the Power Point lesson again.

23
Homework

• In your textbook
• Lesson 4.1/ 1-9, 17, 25