Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply...

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Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Transcript of Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply...

Page 1: Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

GeometryLesson 4 – 2

Angles of Triangles

Objective:Apply the triangle Angle-Sum Theorem.

Apply the Exterior Angle Theorem.

Page 2: Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Triangle Angle-Sum Theorem

Triangle Angle-Sum TheoremThe sum of the measures of the angles of a

triangle is 180.

Page 3: Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Auxiliary line

Auxiliary line – an extra line or segment drawn in a figure to help analyze geometric relationships.

Page 4: Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

ABCGiven :

180321

:Pr

mmm

ove

Page 5: Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Find the measure of each numbered angle.

Which angle do we find first?

Could find angle 2 first since we Know 2 other angles in that triangle. Or we could find angle 1 since we Know it forms a linear pair with 57.

18071572 m1801282 m522 m

180571 m1231m

Since linear pair. Don’t get this 180 confused with adding all the angles of a triangle to 180.

1802813 mm180281233 m1801513 m293 m

Page 6: Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Find the measure of each numbered angle.

18065587 m1801237 m577 m

18076 mm180576 m1236 m

575 m

1806754 mm18067574 m1801244 m564 m

180986 mmm18088123 mm57)8(2 m5.288 m5.289 m

Page 7: Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Exterior & Remote interior angles

Exterior angles of a triangle:Formed by one side of the triangle and the

extension of an adjacent side. Exterior angle that is adjacent to the triangle.

Remote Interior anglesThe 2 interior angles inside the triangle that are not

adjacent to the exterior angle.

Page 8: Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

1 2

34

5

6

7

891011

12

Name an exterior angle and the pairof remote interior angles that go with it.

2&14 Exterior Remote Int.

2&16 3&17 3&19 3&210 3&212

Angles 5, 8, and 11 are not exterior angles since they are not adjacent to a side of the triangle.

Page 9: Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Theorem

Exterior Angle TheoremThe measure of an exterior angle of a

triangle is equal to the sum of the measures of the two remote interior angles.

Page 10: Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Find the measure of angle FLW.

2x – 48 = x + 32 Exterior angle = Sum of Remote Interior angles

x – 48 = 32x = 80

11248)80(2482 xFLW

Page 11: Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Corollary

Corollary – A theorem with a proof that follows as a

direct result of another theorem.

Page 12: Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Corollaries

Corollary 4.1The acute angles of a right triangle are

complementary.

Corollary 4.2There can be at most one right or obtuse

angle in a triangle.

Page 13: Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Find the measures of each numbered angle.

18052901 m1801421 m381m18038902 m1801282 m522 m9023 mm90523 m383 m

1809034 mm18090384 m1801284 m524 m

90382 mor

Page 14: Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Find the measures of each numbered angle.

90415 m495 m

90483 m423 m

56

104

1801052 m762 m

1041m

1805624 mm18056764 m1801324 m484 m

Page 15: Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Homework

Pg. 248 1 – 11 all, 12 – 40 EOE, 50, 60, 64, 66


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