# ANGLES IN TRIANGLES LESSON 16(3).

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ANGLES IN TRIANGLES LESSON 16(3)

TYPES OF TRIANGLES ACUTE TRIANGLE - a traingle with three acute angles. RIGHT TRIANGLE - a triangle with a right angle. ( 90o angle) OBTUSE TRIANGLE - a triangle with an obtuse angle. SCALENE TRIANGLE - no sides are the same, no angles are the same. ISOSCELES TRIANGLE - two sides are the same, base angles are the same. EQUILATERAL TRIANGLE - all sides are the same, all angles are the same. ( 60o )

SUM OF ANGLES IN TRIANGLES
The sum of the angles in a triangle is 180o. PROOF: Using Parallel Lines. 1 =  4 and  3 =  5 But  1 +  2 +  3 = 180o If  1 is replaced with  4 and  3 with  5, then  4 +  2 +  5 = 180o (Z pattern) (straight angle)

EXTERNAL ANGLE OF A TRIANGLE
An exterior (or external) angle is the angle between one side of a triangle and the extension of an adjacent side External angle

EXTERNAL ANGLE OF A TRIANGLE
PROPERTIES: An exterior angle of a triangle is equal to the sum of the opposite interior angles. In the figure below the exterior angle 1 is equal to the sum of the angles 3 and 4  1 =  3 +  4 External angle

Write an equation for the exterior angle of the triangle.
YOU TRY

SOLUTION Exterior angle xo = zo + wo
Write an equation for the exterior angle of the triangle. SOLUTION Exterior angle xo = zo + wo

Calculate the measures of the unknown angles. State how you know.
YOU TRY

SOLUTION  t = 30o ( sum of triangle )  s = 50o ( sum of triangle )
Calculate the measures of the unknown angles. State how you know. SOLUTION  u = 60o ( supplement to 120o )  t = 30o ( sum of triangle )  s = 50o ( sum of triangle )  r = 130o ( supplement to so )

Class work Check solutions to Lesson 16(2)
Copy down notes and examples from this lesson. Do Lesson 16(3) worksheet