Course: Applied Geometry Aim: Understanding Triangles - I 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 

Course: Applied Geometry Aim: Understanding Triangles - I 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 (180 0 ) Right Triangle - has one right angle Acute Triangle - has three acute angles Obtuse Triangle - has one obtuse angle Equiangular Triangle - has three equal angles Classified According to Angles hypotenuse

Course: Applied Geometry Aim: Understanding Triangles - I Model Problems Identify each triangle using its angles.  ABC has angles that measure 100 o, 40 o and  DEF has angles that measure 60 o, 70 o and 50 o.  STU has angles that measure 60 o, 60 o and 60 o.  XYZ has angles that measure 130 o, 20 o and 30 o.  BAC in  ABC measure 60 0 and is equal to  ABC.  BAC in  ABC measure 90 o and  BAC and  BCAare not equal to each other. isosceles equilateral equilangular acute obtuse rt. triangle

Course: Applied Geometry Aim: Understanding Triangles - I 3 equal 2 equal No equal sides sides sides Triangles Classified According to Sides An Equilateral Triangle is also Equiangular A C B 60 0

Course: Applied Geometry Aim: Understanding Triangles - I Model Problems Identify each triangle as equilateral, isosceles or scalene.  ABC has sides that measure 3, 3, and 3 units in length.  HIJ has sides that measure 4, 4, and 7 units in length.  STU has sides that measure 2, 3, and 4 units in length. Line segment AB in  ABC is equal to line segment AC and 4 times the length of line segment BC. Line segment XY in  XYZ is equal to line segments YZ and XZ. equilateral scalene isosceles

Course: Applied Geometry Aim: Understanding Triangles - I Model Problems What type of triangle is each of the following? isosceles right triangle equilateral/equiangular obtuse/scalene

Course: Applied Geometry Aim: Understanding Triangles - I Model Problems Identify the measure of each unknown angle and the type of triangle. x = 180 – ( ) = 79 scalene and acute x = 180 – ( ) = 40 scalene and obtuse x = 180 – ( ) = 80 isosceles and acute x = 180 – ( ) = 60 equilateral/equiangular

Course: Applied Geometry Aim: Understanding Triangles - I Right Triangle ABC If  B = 45 0, then  A = ? C B A If  B = 16 0, then  A = ? If  A = , then  B = ? In right triangle LMN, find the value of x and the measure of  L and  N. M L N x0x0 2x02x0 x + 2x + 90 = 180 3x + 90 = 180 3x = 90 x = 30  L =  N = What is true about  A &  B? complementary angles The sum of the measure of the angles of a triangle is

Course: Applied Geometry Aim: Understanding Triangles - I Find the value of  x,  y, and  z F J G x0x0 y0y0 z0z To find x, use  FJG: x = 180 x or  FJG = x = 180 H To find y, use  FJH, a straight angle:  FJG +  GJH = y = y = To find z, use  GJH: z = 180 z or  FHG = z = 180

Course: Applied Geometry Aim: Understanding Triangles - I In triangle ABC, find the value of x and m  B and  C. C A B x -10x + 15 The sum of the measure of the angles of a triangle is x x = 180 x + 2x = 180 3x + 81 = 180 3x = 99 x = 33  C = x + 15 = 48 0  B = 2x -10 = = = 56 0

Course: Applied Geometry Aim: Understanding Triangles - I Model Problems Identify the measure of each unknown angle. m  1 = m  2 = m  3 = m  4 = m  5 = m  6 = m  7 = m  8 =