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Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem What are we learning? Students will… Classify triangles and find the measures of their angles. Use exterior angles of triangles to solve problems. Evidence Outcome: Prove geometric theorems (lines, angles, triangles, parallelograms). Purpose (Relevancy): This concept is used to find the reclining angle of a lazy boy chair. Finding Angle Measures in Triangles C 50° 35° A B Theorem 3-12: Triangle Angle-Sum Theorem: The sum of the measures of the angles of a triangle is 180. mA mB mC 180 Finding Angle Measures in Triangles C 50° A Find the measure of the three angles. Justify your work. 35° B Finding Angle Measures in Triangles Find the values of x, y, and z. Justify your work. G 39° 21° 65° x° y° z° F J H Finding Angle Measures in Triangles B Find the values of x, y, and z. x°y° z° 49° 62° A C D Classifications of Triangles Equiangular All 's are Acute All 's acute Equilateral All sides Right One right Obtuse One obtuse Isosceles At least 2 sides Scalene No sides Classifications of Triangles Classify the following triangles by their angles and sides. 37° 37° Draw an equilateral right triangle. NOT POSSIBLE!!! Using Exterior Angles of Triangles Exterior Angle of a Polygon: An angle formed by a side and an extension of an adjacent side. Exterior Angle 2 1 3 Remote Interior Angles Remote Interior Angles: The two nonadjacent interior angles corresponding to each exterior angle of a triangle. Using Exterior Angles of Triangles 2 1 3 Theorem 3-13: Triangle Exterior Angle Theorem: The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. m1 m2 m3 Using Exterior Angles of Triangles 100° x° Find the measure of the x. Justify your work. 50° Using Exterior Angles of Triangles Find the values of w, x, y, and z. x° 97° y° 53° w°86° z° Little More Practice Find the value of x. (80 – 2x)° (70 – 3x)° (3.4): Parallel Lines and the Triangle Angle-Sum Theorem HOMEWORK: (3.4): Pgs. 150-152; 2-26 even, 32, 34, 40 Homework Quiz Next Class! TERMS: equiangular Δ, acute Δ, right Δ, obtuse Δ, equilateral Δ, isosceles Δ, scalene Δ. Remember, with great power, comes great responsibility. -Uncle Ben