Bellwork Solve for the variable. x2 + 6x + 5 = 0 b2 – 2b – 15 = 0 m2 – 12 = m

Bellwork Read pages 224-226 of textbook. Complete problems 12-19.

Unit 4 Classifying Triangles 4.2 OBJECTIVE: Classify triangles according to:  angle measures  side lengths Classifying by angles Acute: All angles acute Equiangular: All angle  Right: One right angle Obtuse: One obtuse angle Classifying by side lengths Isosceles: At least 2 sides  Scalene: No sides  Equilateral: All sides 

Unit 4 Classifying Triangles 4.2 Classify the triangle by its sides and its angles. The three sides of the triangle have three different lengths, so the triangle is scalene. One angle has a measure greater than 90, so the  is obtuse. The triangle is an obtuse scalene triangle. Two sides of the triangle are congruent, so the triangle is an isosceles. All angles are acute, so the  is acute. The triangle is an acute isosceles triangle.

Unit 4 Classifying Triangles 4.2 Classify each triangle by its angles and sides. 1. ∆MNQ 2. ∆NQP 3. ∆MNP 4. Find the side lengths of the triangle. acute; equilateral obtuse; scalene acute; scalene 29; 29; 23

Objectives Unit 4 Angle Relationship in Triangles 4.3 Find the measures of interior angles in a triangle. Find the measures of exterior angles in a triangle. Use theorems of triangles to find angle measurements. Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180. mA + mB + mC = 180 A C B

Unit 4 Angle Relationship in Triangles 4.3 2 1 3

Unit 4 Angle Relationship in Triangles 4.3 Example 1: Find mZ. mX + mY +mZ = 180 Triangle Angle-Sum Theorem 48 + 67 + mZ = 180 Substitution 115 + mZ = 180 Simplify. mZ = 65 SPE

Unit 4 Angle Relationship in Triangles 4.3 In triangle ABC, ACB is a right angle, and CD  AB. Find the values of a, b, and c. The measure of one of the acute angles in a right triangle is 63.7°. What is the measure of the other acute angle?

Unit 4 Angle Relationship in Triangles 4.3 Find the value of each variable 74° r s t u 50°

Unit 4 Angle Relationship in Triangles 4.3 Find the value of each variable and the angles of the triangle. 4x (x + 15) y

Unit 4 Angle Relationship in Triangles 4.3 3 is an interior angle. An interior angle is formed by two sides of a triangle. An exterior angle is formed by one side of the triangle and extension of an adjacent side. 4 is an exterior angle. Interior Exterior

Unit 4 Angle Relationship in Triangles 4.3 1 2 3 4 5 6 7 8 Identify the exterior angles

Unit 4 Angle Relationship in Triangles 4.3 Triangle Ext. Angle Thm. The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles m1 = m4 + m3 3 4 1 Exterior Angle Remote Interior Angles

Unit 4 Angle Relationship in Triangles 4.3 Find m 1. Find mB.

Unit 4 Angle Relationship in Triangles 4.3 Other tidbits in this section… If two angles of one triangle are equal to two angles of another triangle, then the 3rd pair of angles are congruent. The measure of each angle of an equiangular triangle is 60°. The acute angles of a right triangle are complementary.

Homework 4.2(227): 21-22, 30-34,47,48 22)2 30) isos,obt 32) 4 34) no,yes 48)8 4.3(235): 19-24,26,28-32 20) 61 22)128° 26)50° 30) 48° 32) 42°