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Transcript
Geometry Section 4-1A Angles Inside the Triangle Pg. 242 1 Tessellations Tessellation: A repeating pattern of figures that completely covers a plan region without gaps or overlaps. We will soon investigate several geometric figures to see whether or not they can be used to tessellate a plane. 2 3 4 Triangles Triangle: A figure formed by three segments that connect three noncollinear points. vertex Pg. 242 Label the parts of the triangle. side side vertex vertex side 5 Triangle Classification by Sides Scalene Triangle – no congruent sides. Isosceles Triangle – 2 congruent sides. Pg. 243 Equilateral Triangle – All sides congruent. 6 Triangles vertex angle Non-right triangles Pg. 244 base angle base base angle leg Right triangles leg 7 Try It: Pg. 244 Try it: Two angles of a triangle measure 40o and 58o. What is the measure of the third angle? 180 – (40 + 58) = 82o 8 Triangle Classification by Angles: Acute Triangle – all angles acute. Obtuse Triangle – 1 obtuse angle. Pg. 244 Equiangular Triangle – All angles congruent. 9 Triangle Angle-sum Theorem Triangle Angle-Sum Theorem: The sum of the measures of the angles of a triangle is 180o. http://mathopenref.com/triangleinternalangles.html 10 Exercises Name and classify each triangle, using both angle and side classification. J N L M #1, 2 Pg. 245 rJLM Isosceles Right O P rNOP Scalene Obtuse 11 Exercises Name and classify each triangle, using both angle and side classification. P Q T #3,4 4.3 Pg. 245 S R rPQR Equilateral Equiangular 3.6 5.0 U rSTU Scalene Acute 12 Exercises Is it possible for each type of triangle to exist? If so, sketch it. If not, explain why. Obtuse Isosceles #6 Pg. 245 13 Exercises Is it possible for each type of triangle to exist? If so, sketch it. If not, explain why. Right Equilateral #7 Pg. 245 Not possible. In an equilateral triangle, every angle is 60o. 14 Exercises Is it possible for each type of triangle to exist? If so, sketch it. If not, explain why. Right Scalene #8 Pg. 245 15 Exercises FP is one side of a triangle on the grid. List the possibilities for the third vertex if the triangle is a: a. obtuse B, C, D, E, V, W, X, Y #9 b. right Pg. 246 c. isosceles H, L, M, N, O, R G, H, I, J, L, Q, R, S, T d. Suppose the third vertex of the triangle is chosen randomly from the points shown in red. What is the probability that the triangle will be a right triangle? 3 4 16 Exercises Find the measure of angle 1. 1 1 #11, 12 Pg. 246 72o 40o 57o 180 – (40 + 72) = 68o 180 – (90 + 57) = 33o 17 Exercises Find the measure of angle 1. 81o #13, 14 1 a 41ao 50o b Pg. 246 1 50o 41o a and b are corresponding ’s and are @. 180 – (81 + 41) = 58o 50o a must = 40o. a + b = 90o therefore, b = 50o and c = 50o 180 – (50 + 50) = 80o 18 Homework: Practice 4-1A #1-3 – You cannot “name” them. Mistake on worksheet. 19