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Transcript
Notes 4B: Triangle Angle Measures Vocabulary: When the sides of a triangle are extended, the angles that are adjacent to the interior angles are exterior angles. <d, <e, <f are the exterior angles of the triangle e d f Theorem 4.2 Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. e d=a+b e=b+c f=a+c a b c d f Corallary to the Triangle Sum Theroem The acute angles of a right triangle are complimentary. a+b+c=180o b 90o +b+c=180o b+c=90o a c Find the value of the missing angles. 1. 2. x x y 53 o y 60o 3. y 68o x 102o Theorem 4.6 Base Angle Theorem If two sides of a triangle are congruent then the angles opposite the sides are congruent. Theorem 4.7 Converse of The Base Angle Theorem If two angles of a triangle are congruent, then the sides opposite them are congruent. Thm. 4.6 Thm. 4.7 a a If Then... If Then... <b = <c b c b c ab=ac 9Use the information provided in the drawing to find x and y. 1. y 2. 50o y 26o x x *3. *4. x o 140 95o x y y Finding missing angles in Triangles with Vertical and Linear Pairs: *Linear Pair:______________________ 4 1 3 2 Vertical Angles:______________________ Use the information provided in the drawing to find x and/or y. 1. 2. Finding missing angles with Equilateral Triangles: Equilaterial:______________________ 3 Equiangular:______________________ 2 1 Use the information provided in the drawing to find x and/or y. 1. 2. Let's practice! Find x and y: 3. 4. 5. xo yo Assignment: Worksheet 4B