Download 2016-12-12 Triangle Sum Theorem.notebook

2016­12­12 Triangle Sum Theorem.notebook
December 12, 2016
Monday,
12/12/2016
Do Now:
- Take out your notebooks
- Copy tonight's HW
Triangle Sum Theorem Worksheet
Classification of Triangles:
1) Equilateral Triangle­ a triangle with three angles equal in measure and three congruent sides.
2) Isosceles Triangle­ a triangle with only two angles equal in measure
and only two congruent
sides
3) Scalene Triangle­ a triangle with no angles
equal in measure and no
congruent sides Also:
right triangle­ with one right angle
acute triangle­ with three acute angles
obtuse triangle­ with one obtuse angle
2016­12­12 Triangle Sum Theorem.notebook
December 12, 2016
What Will Happen??
The sum of the three interior angles in any triangle is 180 degrees
180
180
2016­12­12 Triangle Sum Theorem.notebook
December 12, 2016
Find the missing angle measure. Use an equation.
A x
C
105
35
B
Find x. Then find the other missing angle measure. Use an equation.
P
99
2x
Q
x
R
2016­12­12 Triangle Sum Theorem.notebook
December 12, 2016
How can you classify triangle RST?
R
Write an equation to help you find
measure R.
x
m R =
70
70
T
S
PRACTICE
Find the value of x and classify the triangle.
1. 2.
23
45o
x
38
x
2016­12­12 Triangle Sum Theorem.notebook
December 12, 2016
PRACTICE
Find the value of x and classify the triangle.
3. 4.
60
45
x
60
x
46
2016­12­12 Triangle Sum Theorem.notebook
December 12, 2016
2016­12­12 Triangle Sum Theorem.notebook
December 12, 2016
HOMEWORK: Worksheet #4
1. Isosceles/Acute 2. Scalene/Right 3. Isosceles/Obtuse
4. x = 65 5. y = 40 6. r = 30 7. x = 30 8. y = 42
9. m = 25 10. t = 70 11. x = 40 12. n = 65 13. x = 36
3x = 108
x = 36
2016­12­12 Triangle Sum Theorem.notebook
5­3
December 12, 2016
Objective:
To use Exterior Angle Theorem
to
Solve for Missing Angle Measures Exterior and Interior Angles
2016­12­12 Triangle Sum Theorem.notebook
December 12, 2016
Interior Angle of a triangle is an angle formed by two sides.
Exterior Angle is an
angle formed by one
side and the extension
of an adjacent side.
(next to)
Remote Interior Angle is an
interior angle not adjacent to the exterior angle.
1. Draw triangle ABC. Label the angles 1, 2 and 3.
2. Extend the base at C and label the exterior angle 4.
B
3. m 1 + m 2 + m 3 = _____________
4. 3 and 4 form a ______________,
so m 3 + m 4 = _______________.
A
5. m 1 + m 2 + _________ = ________ + m 4
6. Simplify the equation. 7. The Exterior Angle Theorem states: The measure of an
_____________ angle is equal to the sum of its ______________________________ angles. C
2016­12­12 Triangle Sum Theorem.notebook
December 12, 2016
In a triangle, the measure of the exterior angle is equal to the sum of the measures of the two remote interior angles.
Solve for x. Use an equation.
R
45
x
55
T
Find x.
x
60
25
S
2016­12­12 Triangle Sum Theorem.notebook
R
Use the Exterior Angle Theorem to find the measure of the each angle in the diagram
4x
T
7x
December 12, 2016
7x 110
S
2016­12­12 Triangle Sum Theorem.notebook
December 12, 2016
Warmup: Find the missing angle measure p.
Be careful...this is tricky!
WORKSHEET #4 SIDE 2
Work on this with a partner!
Use Exterior Angle Theorem!
Write an Equation.
Show ALL work!
2016­12­12 Triangle Sum Theorem.notebook
December 12, 2016
HOMEWORK: Worksheet #4
Side 2
1. x = 70 2. x = 65 3. x = 120
4. x = 105 5. x = 95 6. x = 30 7. x = 86 8. x = 130 9. x = 12 Unit 5­3
Objective:
To use Triangle Sum Theorem/Angle Sum Theorem
and Exterior Angle Theorem to Solve for Missing Angle Measures
(REVIEW)
2016­12­12 Triangle Sum Theorem.notebook
EXTRA PRACTICE:
p. 168­ 169
December 12, 2016
2016­12­12 Triangle Sum Theorem.notebook
December 12, 2016
Unit 5­3
Objective:
To use Triangle Angle Theorems, Expressions and Equations
to
Solve for Missing Angle Measures Use the Exterior Angle Theorem to find the measure of the each angle in the diagram
F
D
(3x + 20)
x = 10
m F = 95
m D = 45
m E = 50 (8x + 15)
(4x + 5)
E
2016­12­12 Triangle Sum Theorem.notebook
December 12, 2016
Use the Exterior Angle Theorem to find the measure of the each angle in the diagram
(3x ­10)
25
(x + 15)
Extra Practice: p. 120 from workbook.
T
3.
(7x + 4)
V
(2x + 5)
U
(5x + 3)
2016­12­12 Triangle Sum Theorem.notebook
December 12, 2016
4.
1 n)
( 2
Y
X
n
Z
D
5.
4y
C 1 n)
( 2
(7y+ 6)
116
E
2016­12­12 Triangle Sum Theorem.notebook
December 12, 2016
p.120 #6. Write an equation using the exterior angle theorem and find the measure of the all the angles
23z
(18z + 3)
32