Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

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Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

What are we learning? Purpose: Students will classify triangles, find the measures of their angles, and 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.

Finding Angle Measures in Triangles C 50° 35° A B Find the measure of the three angles. Justify your work.

Finding Angle Measures in Triangles Find the values of x, y, and z. Justify your work. 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° 62° z° 49° A C D

Classifications of Triangles Equiangular Acute Right Obtuse Equilateral Isosceles Scalene

Classifications of Triangles Classify the following triangles by their angles and sides. 3 in. 4 in. 5 in. 7 cm. 16 cm. 106° 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. Remote Interior Angles Exterior Angle 1 2 3 Remote Interior Angles: The two nonadjacent interior angles corresponding to each exterior angle of a triangle.

Using Exterior Angles of Triangles 1 2 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.

Using Exterior Angles of Triangles 100° x° 50° Find the measure of the x. Justify your work.

Using Exterior Angles of Triangles Find the values of w, x, y, and z. 97° x° y° 53° w° 86° z°

Little More Practice Find the value of x. (80 – 2x)° (70 – 3x)°

and the Triangle Angle-Sum Theorem (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