3.4 Angles in a Triangle Objective â&#x20AC;&#x201C; Classify triangles by sides and angles. Find angle measures of triangles.

What do we need to know about triangles? v ertex

side

v ertex

side

side

v ertex

Triangle Classification by Sides • Scalene Triangle B

A

X

C

• Isosceles Z Q

• Equilateral P

R

Y

Triangle Classification by Angles • Acute • all angles are acute

• Obtuse • one obtuse angle

• Right • one right angle

• Equiangular • all angles are the same

Theorem โข The sum of the measures of the angles of a triangle is 180ยบ

What is a corollary?

â&#x20AC;˘ A statement that can be proved easily by applying a theorem.

First Corollary • If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent E

B

F

A

C

D

• If m∠ A = m∠D and m∠B = m∠E, then what can we say? • m∠ C = m∠F

Second Corollary • Each angle of an equiangular triangle has a measure of ___. • 180 ÷ 3 • 60º

Third Corollary â&#x20AC;˘ In a triangle, there can be at most one right angle or obtuse angle.

â&#x20AC;˘ Why?

Fourth Corollary • The acute angles of a right triangle are ________. • Complementary • Why?

Notebooks â&#x20AC;˘ The rest of your notes will have to be taken in your notebook!

Remote Interior Angles

100

70

30

Exterior Angle Theorem â&#x20AC;˘ The measure of an exterior angle of a triangle equals the sum of the two remote interior angles.

Find the measure of angle A for each. 1)

2) 80

80 40 120

50

A

A

Find x and y. x

60

П

y

Find x and y. 50

60

x

45

y

Homework… • Page 97; 5-14

Notes 3.4
Notes 3.4

Finding measures of Triangles