lesson 3: (3.4) parallel lines and the triangle angle-sum theorem

Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

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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.

Page 3: Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

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

50° 35°

Page 4: Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

Finding Angle Measures in Triangles

50° 35°

Find the measure of the three angles. Justify your work.

Page 5: Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

Finding Angle Measures in Triangles

HJ65°

39° 21°

x° y° z°

Find the values of x, y, and z. Justify your work.

Page 6: Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

Finding Angle Measures in Triangles

DC62° 49°

x° y°

z°

Find the values of x, y, and z.

Page 7: Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

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

Page 8: Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

Classifications of Triangles

3 in.

4 in

5 in.

7 cm

7 cm.

16 cm.

106°

37°

Classify the following triangles by their angles and sides.

Draw an equilateral right triangle.

NOT POSSIBLE!!!

Page 9: Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

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

Page 10: Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

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

Page 11: Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

Using Exterior Angles of Triangles

x°

100°

50°

Find the measure of the x. Justify your work.

Page 12: Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

Using Exterior Angles of Triangles

53° w° 86°

x°y°

z°

Find the values of w, x, y, and z.97°

Page 13: Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

Little More Practice

(80 – 2x)°

(70 – 3x)°

Find the value of x.

Page 14: Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

(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.

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