6/24/2010 ©Evergreen Public Schools 2010 1 Triangle Sum Theorem Vocabulary : flowchart theorem.
Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem.
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Transcript of Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem.
Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem
What are we learning?
Purpose:Students will classify triangles, find the measures of their angles, and use exterior angles of triangles to solve problems.
Evidence Outcome: Prove geometric theorems (lines, angles, triangles, parallelograms).
Purpose (Relevancy): This concept is used to find the reclining angle of a lazy boy chair.
Finding Angle Measures in Triangles
Theorem 3-12: Triangle Angle-Sum Theorem: The sum of the measures of the angles of a triangle is 180.
mA mB mC 180
A
C
B
50° 35°
Finding Angle Measures in Triangles
A
C
B
50° 35°
Find the measure of the three angles. Justify your work.
Finding Angle Measures in Triangles
F
G
HJ65°
39° 21°
x° y° z°
Find the values of x, y, and z. Justify your work.
Finding Angle Measures in Triangles
A
B
DC62° 49°
x° y°
z°
Find the values of x, y, and z.
Classifications of Triangles
Equiangular
All 's are Acute
All 's acuteRight
One right Obtuse
One obtuse
Equilateral
All sides Isosceles
At least 2 sides Scalene
No sides
Classifications of Triangles
3 in.
4 in
.
5 in.
7 cm
.
7 cm.
16 cm.
106°
37°
37°
Classify the following triangles by their angles and sides.
Draw an equilateral right triangle.
NOT POSSIBLE!!!
1
2
3
Using Exterior Angles of Triangles
Exterior Angle
Exterior Angle of a Polygon: An angle formed by a side and an extension of an adjacent side.
Remote Interior Angles: The two nonadjacent interior angles corresponding to each exterior angle of a triangle.
Remote Interior Angles
Using Exterior Angles of Triangles
Theorem 3-13: Triangle Exterior Angle Theorem: The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
m1m2 m3
1
2
3
Using Exterior Angles of Triangles
x°
100°
50°
Find the measure of the x. Justify your work.
Using Exterior Angles of Triangles
53° w° 86°
x°y°
z°
Find the values of w, x, y, and z.97°
Little More Practice
(80 – 2x)°
(70 – 3x)°
Find the value of x.
(3.4): Parallel (3.4): Parallel Lines Lines
and the Triangle and the Triangle Angle-Sum Angle-Sum TheoremTheorem
Remember, with great power, comes great responsibility.-Uncle Ben
HOMEWORK: (3.4): Pgs. 150-152; 2-26 even, 32, 34, 40Homework Quiz Next Class!
TERMS: equiangular Δ, acute Δ, right Δ, obtuse Δ, equilateral Δ, isosceles Δ, scalene Δ.