Triangles

is the symbol for triangle. A triangle is a polygon (a figure) that has three sides, three vertices, and three angles. A vertex is the endpoint that joins the sides of a triangle. Sides: AB, BC, CA A Angles: A, B, C, is the symbol for triangle. B C Vertices: A, B, C A triangle is named with the three vertices in any order. A triangle is named with the three vertices in any order. ABC, BCA, or CAB

’s can be classified in two ways: (1) by their sides and/or (2) by their angles Method 1: Classifying ’s by Sides Equilateral Triangle Isosceles Triangle Scalene Triangle All sides are congruent Two sides are congruent No sides are congruent.

Method 2: Classifying ’s by Angles Equiangular Triangle Acute Triangle Obtuse Triangle Right Triangle All angles are acute (each angle is less than 90o) All angles are congruent One obtuse angle (between 90o – 180o). One right angle

Equiangular Equilateral  Ex. 1 Classify the triangles by its angles and its sides. Explain. a) b) 60o Equiangular Equilateral  60o 60o Right Isosceles 

c) Obtuse Scalene  120o

Open your textbooks Pg 174 #4,6 Pg 175 # 2-10 (even) Pg176 #12 – 22 (even) Pg 177 #30-36 (even) Pg178 # 42, 54, 55, 56

Exterior and Interior Angles Interior Angles: 3 original angles (the angles that are inside the triangle). 4 1 6 3 1, 2, 3 are interior angles C Exterior Angles: angles that are adjacent to the interior angles (they form a linear pair with the interior angles) 2 5 B 4, 5, 6 are exterior angles

Triangle Sum Theorem mA + mB + mC = 180o The sum of the measures of the interior angles of a triangle is 180o. A mA + mB + mC = 180o B C

25 + 95 + C = 180o  sum theorem 120+ C = 180o C = 180 - 120 Ex. 1 Given mA = 25o and mB = 95o, find the mC? 25 + 95 + C = 180o  sum theorem 120+ C = 180o A B C = 180 - 120 C = 60o C

Ex. 2 Find the value of x. C + B + A = 180o (5x + 3)o + (47o) +(90o) = 180o A B C (5x + 3) + 137 = 180 5x + 3 = 180-137 5x + 3= 43 5x = 43 – 3 5x=40 x = 40/5 x = 8

Find x, then find the m ∠B. A B C

39 + 65 + x = 180 Triangle sum theorem 104 + x = 180 Ex. 3 Find the values of x and y. To find the value of x, use GFJ G 21o 39 + 65 + x = 180 Triangle sum theorem 39o 104 + x = 180 x = 180 - 104 x = 76o 65o 76o xo yo To find the value of y; look at FJH. F H J x + y = 180 linear pair 76 + y = 180 y = 180 – 76 y = 104o

Exterior Angles Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. m1 = mA + mB A B 1

Ex. 4 Find each missing angle measure. b. m A = 40 + 30 ext.  `s thm 40o m A = 70o A 30o 113 = m B + 70 ext.  `s thm 70o 113o 113 – 70 = B m B = 43o B

A + B = C (6x -1) + (5x + 17) = 126 11x + 16 =126 11x = 110 X = 10 Ex. 5 Find the value of x. A =C B A + B = C (6x -1) + (5x + 17) = 126 11x + 16 =126 11x = 110 X = 10

Find x.

Class Work Pg 182 #4-14 (even) Pg 183 #18, 20 Pg 184 #25, 2, 4, 6