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Transcript
Aim: Understanding Triangles Do Now: SAT Question What must be the complement of the supplement of an obtuse angle? A. An acute B. A right C. An obtuse D. A straight E. A reflex Aim: Understanding Triangles - I Course: Applied Geometry Triangles A triangle is a three sided polygon enclosing three angles. The sum of the measure of the angles of a triangle is 180 degrees (1800) Classified According to Angles Right Triangle - has one right angle Acute Triangle - has three acute angles Obtuse Triangle - has one obtuse angle Applied Geometry Aim: Understanding Triangles - I Equiangular Triangle - has three Course: equal angles Model Problems Identify each triangle using its angles. ABC has angles that measure 100o, 40o and isosceles 400. DEF has angles that measure 60o, 70o and acute 50o. STU has angles that measure 60o, 60o and equilangular 60o. XYZ has angles that measure 130o, 20o and obtuse 30o. BAC in ABC measure 600 and is equal to equilateral ABC. BAC in ABC measure 90o and BAC and Course: Applied Geometry Aim:equal Understanding rt. triangle BCAare not to Triangles each- Iother. Triangles Classified According to Sides 3 equal sides 2 equal sides No equal sides C •An Equilateral Triangle is also Equiangular 600 A 600 Aim: Understanding Triangles - I 600 Course: Applied Geometry B Model Problems Identify each triangle as equilateral, isosceles or scalene. ABC has sides that measure 3, 3, and 3 equilateral units in length. HIJ has sides that measure 4, 4, and 7 units isosceles in length. STU has sides that measure 2, 3, and 4 units in length. scalene Line segment AB in ABC is equal to line segment AC and 4 times the length of line isosceles segment BC. Line segment XY in XYZ is equal to line equilateral segments YZAim:and XZ. Course: Applied Geometry Understanding Triangles - I Model Problems What type of triangle is each of the following? equilateral/equiangular obtuse/scalene isosceles right triangle Aim: Understanding Triangles - I Course: Applied Geometry Model Problems Identify the measure of each unknown angle and the type of triangle. B x=? x x = 180 – (55 + 46) = 79 scalene and acute 46 55 C A B x=? x 25 115 A A C 50 50 y=? C x = 180 – (25 + 115) = 40 scalene and obtuse y B x = 180 – (50 + 50) = 80 isosceles and acute C 60 A t=? 60 Aim: t B x = 180 – (60 + 60) = 60 equilateral/equiangular Course: Applied Geometry Understanding Triangles - I Right Triangle ABC B If B = 450, then A = ? 450 If B = 160, then A = ? 740 If A = 33.50, then B = ? 56.50 C What is true about A & B? complementary angles A The sum L of the In right triangle LMN, find the value measure of the of x and the measure of L and N. 0 x of angles a 0 30 x + 2x + 90 = 180 triangle is 1800. 3x + 90 = 180 600 0 3x = 90 2x x = 30 M N L = 300 N = 600 Aim: Understanding Triangles - I Course: Applied Geometry Find the value of x, y, and z G To find x, use FJG: 210 390 65 + 39 + x = 180 104 + x = 180 0 x orFJG = 76 0 650 x0 y z0 F J H To find y, use FJH, a straight angle: FJG + GJH = 1800 760 + y = 1800 y = 1040 To find z, use GJH: 104 + 21 + z = 180 125 + z = 180 z or FHG = 550 Aim: Understanding Triangles - I Course: Applied Geometry In triangle ABC, find the value of x and mB and C. The sum of the measure of the angles of a triangle is 1800. C A 760 x + 15 2x -10 B x + 15 + 2x - 10 + 76 = 180 x + 2x + 15 - 10 + 76 = 180 3x + 81 = 180 3x = 99 x = 33 C = x + 15 = 480 B = 2x -10 = 530 33+ 15 = 480 66 -10 = 560 Aim: Understanding Triangles - I Course: Applied Geometry Model Problems Identify the measure of each unknown angle. A J 36 C 1 61 2 5 F 118 6 3 46 E D 81 4 m3 = 66 B m4 = H 7 8 G m1 = m2 = 51 m5 = m6 = m7 = m8 = Aim: Understanding Triangles - I Course: Applied Geometry