1. ANGLES IN TRIANGLES
LESSON 16(3)

2. 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 )

3. 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)

4. 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

5. 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

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

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

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

9. 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 )

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