3.4 Angles in a Triangle Objective â€“ Classify triangles by sides and angles. Find angle measures of triangles.
What do we need to know about triangles? v ertex
Triangle Classification by Sides • Scalene Triangle B
• Isosceles Z Q
• Equilateral P
Triangle Classification by Angles • Acute • all angles are acute
• Obtuse • one obtuse angle
• Right • one right angle
• Equiangular • all angles are the same
Theorem โข The sum of the measures of the angles of a triangle is 180ยบ
What is a corollary?
â€˘ 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
• 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€˘ In a triangle, there can be at most one right angle or obtuse angle.
Fourth Corollary • The acute angles of a right triangle are ________. • Complementary • Why?
Notebooks â€˘ The rest of your notes will have to be taken in your notebook!
Remote Interior Angles
Exterior Angle Theorem â€˘ 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)
80 40 120
Find x and y. x
Find x and y. 50
Homework… • Page 97; 5-14