1.1. ACUTE TRIANGLEACUTE TRIANGLE - a traingle with three acute - a traingle with three acute

angles.angles.

2.2. RIGHT TRIANGLERIGHT TRIANGLE - a triangle with a right angle. ( 90 - a triangle with a right angle. ( 90oo angle)angle)

3.3. OBTUSE TRIANGLEOBTUSE TRIANGLE - a triangle with an obtuse - a triangle with an obtuse angle.angle.

4.4. SCALENE TRIANGLESCALENE TRIANGLE - no sides are the same, no - no sides are the same, no angles are the same.angles are the same.

5.5. ISOSCELES TRIANGLEISOSCELES TRIANGLE - two sides are the same, - two sides are the same, base angles are the same.base angles are the same.

6.6. EQUILATERAL TRIANGLEEQUILATERAL TRIANGLE - all sides are the same, - all sides are the same, all angles are the same. ( 60all angles are the same. ( 60oo ) )

The The sumsum of the angles in a triangle is of the angles in a triangle is 180180oo..

PROOF: PROOF: Using Parallel Lines.Using Parallel Lines.

1 = 1 = 4 and 4 and 3 = 3 = 5 5

But But 1 + 1 + 2 + 2 + 3 = 180 3 = 180oo

If If 1 is replaced with 1 is replaced with 4 4 and and 3 with 3 with 5, 5,

then then 4 + 4 + 2 + 2 + 5 = 180 5 = 180oo

(Z pattern)(Z pattern)

(straight angle)(straight angle)

An An exterior (or external) angleexterior (or external) angle is the angle between is the angle between one side of a triangle and the extension of an adjacent one side of a triangle and the extension of an adjacent sideside

External angleExternal angle

PROPERTIES:PROPERTIES:

External angleExternal angle

An An exterior angleexterior angle of a triangle is of a triangle is equal to the sumequal to the sum of the of the opposite interior anglesopposite interior angles..

In the figure below the exterior angle In the figure below the exterior angle 11 is equal to the sum is equal to the sum of the angles of the angles 33 and and 44

1 = 1 = 3 + 3 + 4 4

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

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

Exterior angle xExterior angle xoo = z = zoo + w + woo

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

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

1.1. u = 60u = 60oo ( supplement to 120 ( supplement to 120oo ) )

2.2. t = 30t = 30oo ( sum of triangle ) ( sum of triangle )

3.3. s = 50s = 50oo ( sum of triangle ) ( sum of triangle )

4.4. r = 130r = 130oo ( supplement to s ( supplement to soo ) )

Class workClass work

Check solutions to Lesson 16(2)Check solutions to Lesson 16(2) Copy down notes and examples from this Copy down notes and examples from this

lesson.lesson. Do Lesson 16(3) worksheetDo Lesson 16(3) worksheet