1. Triangles and Angles Students will classify triangles by their sides and by their angles. Students will apply the Triangle-Angle Sum Theorem, the Isosceles Triangle Theorem and its converse, linear pair, vertical angles and the Exterior Angle Theorem

2. Types of Triangles Classifying by Side: Equilateral - 3 congruent sides Isosceles - at least 2 congruent sides Scalene - no congruent sides leg base

3. Classifying by Angle: Acute - 3 acute angles Equiangular - 3 congruent angles Right - 1 right angle Obtuse - 1 obtuse angle leg hypotenuse

4. More Vocabulary Interior Angles The three original angles of the triangle. Exterior Angles The angles that are adjacent to the interior angles of the triangle. Theorem 4.1 Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180 0. m  A + m  B + m  C = 180 0 A B C 1 2 3 1 2 3

5. Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary. m  A + m  B = 90 0 A C B

6. 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. m  CBD = m  A + m  C A C 1 BD

7. Vertical Angles Conjecture You will need: a straight edge, patty paper 1. Draw two intersecting lines onto patty paper. Label the angles as shown. Which angles are vertical angles? 1 2 3 4

8. 2. Fold the paper so that the vertical angles lie over each other. What do you notice about their measures? 3. Fold the paper so that the other pair of vertical angles lie over each other. What do you notice about their measures? 4. Compare the results with the results of others. Complete the statement. Vertical Angles Conjecture: If two angles are vertical angles, then ______________. they are congruent

9. Linear Pair Conjecture Using the previous figure – measure the 4 indicated angles with a protractor. What do you notice about the sum of the two adjacent angles (linear pair)? 1 2 3 4 If two angles form a linear pair, then _____________________________________. the measures of the angles add up to 180 o

10. Find the value of x. 1. 2. FE x = 6 x = 11

11. Find the measures of the missing angles 60 o 55 o 65 o a cb d f e hi g a=60 o b=120 o c=120 o d=115 o e=65 o f=115 o g=125 o h=55 o i=125 o