2. 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 

3. 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

4. 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 40 0.  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

5. 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

6. 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

7. 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

8. Course: Applied Geometry Aim: Understanding Triangles - I Model Problems Identify the measure of each unknown angle and the type of triangle. x = 180 – (55 + 46) = 79 scalene and acute x = 180 – (25 + 115) = 40 scalene and obtuse x = 180 – (50 + 50) = 80 isosceles and acute x = 180 – (60 + 60) = 60 equilateral/equiangular

9. 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 = 33.5 0, then  B = ? 56.5 0 74 0 45 0 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 = 30 0 30 0  N = 60 0 60 0 What is true about  A &  B? complementary angles The sum of the measure of the angles of a triangle is 180 0.

10. Course: Applied Geometry Aim: Understanding Triangles - I Find the value of  x,  y, and  z F J G x0x0 y0y0 z0z0 21 0 39 0 65 0 To find x, use  FJG: 104 + x = 180 x or  FJG = 76 0 65 + 39 + x = 180 H To find y, use  FJH, a straight angle:  FJG +  GJH = 180 0 76 0 + y = 180 0 y = 104 0 To find z, use  GJH: 125 + z = 180 z or  FHG = 55 0 104 + 21 + z = 180

11. Course: Applied Geometry Aim: Understanding Triangles - I In triangle ABC, find the value of x and m  B and  C. C A B 76 0 2x -10x + 15 The sum of the measure of the angles of a triangle is 180 0. x + 15 + 2x - 10 + 76 = 180 x + 2x + 15 - 10 + 76 = 180 3x + 81 = 180 3x = 99 x = 33  C = x + 15 = 48 0  B = 2x -10 = 53 0 33+ 15 = 48 0 66 -10 = 56 0

12. 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 =