2. What is a triangle?

3. Triangles can be classified by their angles. There are four different classifications by angles. Equiangular triangles are triangles with three congruent angles. Acute triangles are triangles with three acute angles. Obtuse triangles are triangles with one obtuse angle and two acute angles. Right triangles are triangles with one right angle and two acute angles.

4. WHITE NOTE CARD Triangle Classification by Angles Equiangular - three congruent angles AcuteObtuseRight 3 acute angles1 obtuse angle and 2 acute angles 1 right angle and 2 acute angles

5. Triangles can also be classified by their sides. What is an equilateral triangle? 3 congruent sides 3 acute angles 3 congruent angles

6. Triangles can also be classified by their sides in three different ways. What is an isosceles triangle? 2 congruent sides could be acute, right, or obtuse 2 congruent angles

7. There are three ways to classify triangles by sides. What is a scalene triangle? no congruent sides could be acute, right, or obtuse no congruent angles

8. WHITE NOTE CARD Triangle Classification by Sides EquilateralIsoscelesScalene 3 congruent sides 3 congruent angles Acute triangle 2 congruent sides 2 congruent angles Acute, right, or obtuse No congruent sides No congruent angles Acute, right or obtuse

9. Angle Sum Theorem What is the sum of the measures of the angles in a triangle? Prove that the sum of the angles in a triangle is 180º. º Note card

10. Given: ABC is a triangle. A B C (Number the angles for convenience) 1 2 3 Prove:  1 +  2 +  3 = 180 STATEMENTS REASONS 1. ABC is a triangle 1. Given 2.Draw a line through B that is parallel to AC 2. Parallel Postulate 3.  4 +  2 +  5 = 180 4.  1   4 and  3   5 5.  1 +  2 +  3 = 180 4.If two parallel lines are cut by a transversal then the alternate interior angles are congruent. 5. Substitution Property 45 3. Definition of Supplementary angles Click on the reason for an explanation.  4 +  2 +  5 = 180

11. COLORED NOTE CARD Angle Sum Theorem The sum of the measures of the angles in a triangle is 180º.

13. The Parallel Postulate If you are given a line and a point not on the line, there is exactly one line that can be drawn through the point that is parallel to the line. A B C

14. You can draw this line because it does not change the given information. A B C 1 2 3 Return