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3.4 & 4.5 TRIANGLES 3-4 PARALLEL LINES AND THE TRIANGLE ANGLE-SUM THEOREM Objectives: 1) to classify triangles and find the measures of their angles 2) To use exterior angles of triangles Watch the Video for the Proof of Triangle Angle-Sum Theorem Example 1: Find the values of x, y, and z. You try. Find the values of x, y, and z. You can classify a triangle by its angles and sides. Try these. Draw and mark a triangle to fit each description. If no triangle can be drawn, write not possible and explain why. a) acute scalene a) Isosceles right b) Obtuse equiangular • Exterior angle of a polygon: angle formed by a side and an extension of an adjacent side • Remote interior angles: the two nonadjacent interior angles • Proof of Triangle Exterior Angle Theorem Example 3: Find each missing angle. Try this. Find the measure of angle 1. 125=90+m∠1 35=m∠1 Try this one too. Example 4: Find the value of x. 4-5 ISOSCELES AND EQUILATERAL TRIANGLES Objective: use and apply properties of isosceles triangles What is an Isosceles Triangle? • Isosceles triangle: A triangle with at least two congruent sides • Legs: The congruent sides of an isosceles triangle • Base: The “other” side not counting as the two congruent sides • Vertex angle: The angle included by the two congruent sides • Base angles: The Angles that include the Base Example 5: Solve for Variable a) b) c) d) Try these. Example 6: Apply Concepts Triangle RST is an isosceles triangle. • R is the vertex angle, RS = x + 7, ST = x – 1, and RT = 3x – 5. • Find x, RS, ST, and RT. Now substitute! RT = RS 3x - 5 = x + 7 2x - 5 = 7 2x =12 x=6 RS = 6 + 7 RS = 13 ST = 6 -1 ST = 5 RT = 3(6) - 5 RT =13 Corollary: statement that follows directly from a theorem Example 7: Solve for each variable. Try these.