10/13/14 Geometry Bellwork

4.1 Apply Triangle Sum Properties

10/13/14(Starts on Page 217 in book)

Classification By Sides

Classification By Angles

Classifying Triangles In classifying triangles, be as specific as possible.

Acute,Scalene

Obtuse,Isosceles

Theorem 4.1 Triangle Sum Theorem

The sum of the measures of the interior angles of a triangle is 180o.

32

1

m<1 + m<2 + m<3 = 180°

The sum of all the angles equals 180º degrees.

90º 30º

60º

60º90º30º+

180º

Property of triangles

60º60º60º+

180º60º 60º

60º

The sum of all the angles equals 180º degrees.

Property of triangles

What is the missing angle?

70º70º

?+

180º70º 70º

?

180 – 140 = 40˚

30º78º

?+

180º78º 30º

?

180 – 108 = 72˚

What is the missing angle?

45x 10x

35x

90°, 70°, 20°

Find all the angle measures

180 = 35x + 45x + 10x180 = 90x 2 = x

What can we find out?

The ladder is leaning on the ground at a 75º angle. At what angle is the top of the ladder touching the building?

75

180 = 75 + 90 + x180 = 165 + x

15˚ = x

• Exterior Angles are angles that are on the outside of a figure.

• Interior Angles are angles on the inside of a figure.

Exterior Angles vs. Interior Angles

Theorem 4.2 Exterior Angle Sum Theorem

• The measure of the exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle

Find measure of angle y

88 + 70 = y

158 = y

Find the value of x

• 2x + 40 = x + 72 2x = x + 32 x = 32

Corollary to Triangle Sum TheoremA Corollary is a statement that readily follows from a theorem.

The acute angles of a right triangle are complementary.

m A + m B = 90∠ ∠ o

10/13/14 Geometry Homework

Textbook: Page: 221Exercises: 1-6 All, 14-19 All

Due 10/14/14