Download Adv - Lesson 7.2 - Angle Theorems for Triangles.notebook

Adv ­ Lesson 7.2 ­ Angle Theorems for Triangles.notebook
January 18, 2017
Lesson 7­2
Angles Theorems for Triangles
If you tear off two corners of a triangle and place them next to the third corner, the three angles seem to form a straight line.
Adv ­ Lesson 7.2 ­ Angle Theorems for Triangles.notebook
January 18, 2017
Draw a triangle and extend one side. Then draw a line parallel to the extended side, as shown.
The sides of the
triangle are transversals to the parallel lines.
The three angles in the triangle can be arranged to form a straight line or 180°.
The angle measures of a triangle in a plane add up to 180 0 .
Adv ­ Lesson 7.2 ­ Angle Theorems for Triangles.notebook
January 18, 2017
The angle measures of a triangle in a plane add up to 180 0 .
o
m A + m B + m C = 180
The angle measures of a triangle in a plane add up to 180 0 .
o
m A + m B + m C = 180
This is called the
Triangle Sum Theorem.
Adv ­ Lesson 7.2 ­ Angle Theorems for Triangles.notebook
January 18, 2017
The angle measures of a triangle in a plane add up to 180 0 .
o
m A + m B + m C = 180
This is called the
Triangle Sum Theorem.
o
o
o
42 + 103 + 35 = 180
o
42
o
103
o
35
What do you remember about triangles?
o
Adv ­ Lesson 7.2 ­ Angle Theorems for Triangles.notebook
January 18, 2017
What do you remember about triangles?
An acute triangle has 3 acute angles.
An acute triangle has 3 acute angles.
A right triangle has 1 right angle.
Adv ­ Lesson 7.2 ­ Angle Theorems for Triangles.notebook
January 18, 2017
An acute triangle has 3 acute angles.
A right triangle has 1 right angle.
An obtuse triangle has 1 obtuse angle.
Find p° in the acute triangle.
Remember: There are 3 acute angles.
73° + 44° + p° = 180°
117° + p° = 180°
–117° –117° p° = 63°
Adv ­ Lesson 7.2 ­ Angle Theorems for Triangles.notebook
January 18, 2017
Find c° in the right triangle.
Don't forget a right triangle has
only 1 right angle.
c = _____ Find c° in the right triangle.
Find m° in the obtuse triangle.
Hint: An obtuse triangle Don't forget a right triangle has
has only 1 obtuse angle.
only 1 right angle.
c m = _____
= _____ Adv ­ Lesson 7.2 ­ Angle Theorems for Triangles.notebook
January 18, 2017
An equilateral triangle has 3 congruent sides and 3 congruent angles. Find the angle measures in the equilateral triangle.
3b° = 180° Triangle Sum Theorem An isosceles triangle has at least 2 congruent sides and 2 congruent angles. Find the angle measures in the isosceles triangle.
62° + t° + t° = 180°
Triangle Sum Theorem
A scalene triangle has no congruent sides and no congruent angles.
Find the angle measures in the scalene triangle.
What do I do here?
Adv ­ Lesson 7.2 ­ Angle Theorems for Triangles.notebook
January 18, 2017
A scalene triangle has no congruent sides and no congruent angles.
Find the angle measures in the scalene triangle.
2x° + 3x° + 5x° = 180°
practice
Triangle Sum Theorem
Adv ­ Lesson 7.2 ­ Angle Theorems for Triangles.notebook
January 18, 2017
Finding Angles in a Triangle
Meets
that Given Conditions
Adv ­ Lesson 7.2 ­ Angle Theorems for Triangles.notebook
January 18, 2017
Finding Angles in a Triangle
Meets
that Given Conditions
o
Let x = the first angle measure.
x° + 6x° + 3x° = 180°
Finding Angles in a Triangle
Meets
that Given Conditions
o
Let x = the first angle measure.
o
Then 6x = second angle measure.
x° + 6x° + 3x° = 180°
Adv ­ Lesson 7.2 ­ Angle Theorems for Triangles.notebook
January 18, 2017
Finding Angles in a Triangle
Meets
that Given Conditions
Solve for x.
o
Let x = the first angle measure.
x° + 6x° + 3x° = 180°
o
Then 6x = second angle measure.
o
1 (6x ) = 3x, or third angle measure.
2
Continued
So x = ________
Now find the angle measurements of each angle in the triangle.
x° = the first angle measure.
6x° = second angle measure
o
18
Click
108o
Click
3x° = third angle measure
54o
Click
Adv ­ Lesson 7.2 ­ Angle Theorems for Triangles.notebook
January 18, 2017
Now you try it.....
The second angle in a triangle is three times larger than the first. The third angle is one third as large as the second. Find the angle measures and draw a possible picture.
o
o
o
1st
2nd
3rd
36 108 36
Homework
Worksheet 7.2
(Both Sides)
Quiz
Friday