Classifying Triangles Angles of Triangles

Classifying Triangles Angles of Triangles Notes 16 – Sections 4.1 and 4.2

Essential Learnings • Students will understand and be able to identify and classify triangles by angle and side measures.

Classifying Triangles by Angles • Acute triangle – 3 acute angles • Equiangular triangle – 3 congruent acute angles

Classify Triangles • Obtuse triangle – 1 obtuse angle • Right triangle – 1 right angle

Example 1 • Classify ∆XYZ. X 40° W 50° 40° 50° Z Y

Classifying Triangles by Sides • Equilateral triangle – 3 congruent sides • Isosceles triangle – 2 congruent sides

Classifying Triangles by Sides • Scalene triangle – no congruent sides

Example 2 • Classify each triangle by sides. D is the midpoint of AC and AC = 4. ∆BDC ∆ABD ∆ABC

Example 3 • ∆FGH is an equilateral triangle with FG = x+5, GH = 3x-9 and FH = 2x-2. Find x and the side lengths.

Example 4 • ∆OMG is an isosceles triangle with OM = MG, OM = 5x-1, MG = 2x+14, and OG =3x+2. Find x and the side lengths.

Triangle Angle-Sum Theorem • The sum of the measures of the angles of a triangle is 180.

Example 5 • Find the measure of the numbered angle.

Example 6 • Find the measure of the numbered angles.

Exterior Angle Theorem • The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Example 7 • Find the measure of ∠FLW in the fenced flower garden below.

Example 8 • Find the measures of the numbered angles.

Assignment Pages 239-240: 21-26, 30-37, 40-42, 49, 51 Pages 248-250: 13-21 odd, 24-32, 36, 37 In Class Practice – WS 4.1/4.2 Unit Study Guide 3

Classifying Triangles Angles of Triangles