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

CB

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.

32

1

m<1 + m<2 + m<3 = 180°

The sum of all the angles equals 180º degrees.

90º 30º

60º

60º90º30º+

180º

Property of triangles

90º 50º

40º

40º90º50º+

180º

The sum of all the angles equals 180º degrees.

Property of triangles

60º60º60º+

180º60º 60º

60º

The sum of all the angles equals 180º degrees.

Property of triangles

Ex: 1What is the missing angle?

70º70ºx+

180º70º 70º

x

180 – 140 = 40˚

90º30ºx+

180º30º 90º

x

180 – 120 = 60˚

EX: 2 What is the missing angle?

60º60ºx+

180º60º 60º

x

180 – 120 = 60˚

Ex: 3What is the missing angle?

30º78º

X+

180º78º 30º

X

180 – 108 = 72˚

EX 4:What is the missing angle?

40º40º

?+

180º40º 40º

?

180 – 80 = 100˚

What is the missing angle?

45x 10x

35x

90°, 70°, 20°

Find all the angle measures

180 = 35x + 45x + 10x

180 = 90x

2 = x

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 + x25˚ = x

Extention to Triangle Sum Theorem

The acute angles of a right triangle are complementary.

m A + m B = 90∠ ∠ o

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.

Find the missing angles.

Con’t

Find the missing angles.

2x + x = 90

3x = 90

x = 30˚

2x = 60˚

SOLUTION:

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 workRead 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