1. 4-1 Classifying Triangles SWBAT: Identify and classify triangles by angle measures and side measures. G.6

2. Classifying Triangles by Angles: Recall that a triangle is a three-sided polygon. Triangle ABC, written as ABC, has parts that are named using A,B and C. A B C The sides of ABC are AB, BC, and CA The vertices are points A,B and C. The angles are <BAC or <A, <ABC or <B and <BCA or <C Triangles can be classified in two ways-by their angles or by their sides. All triangles have at least two acute angles, but the third angle is used to classify the triangle.

3. Acute Triangle: 3 acute angles Equiangular Triangle: 3 congruent acute angles Obtuse Triangle: 1 obtuse angle Right Triangle: 1 right angle

4. Classify each triangle as acute, equiangular, obtuse, or right. 70o 40o 30o 60o 30o 120o 20o

5. Classify XYZ as acute, equiangular, obtuse, or right. Explain your reasoning 40o 50o 40o 50o X Y Z W

6. Classifying Triangles by Sides: Triangles can also be classified according to the number of congruent sides they have. To indicate that sides of a triangle are congruent, an equal number of hash marks is drawn on the corresponding sides. Equilateral Triangle: 3 congruent sides Isosceles Triangle: 2 congruent sides Scalene Triangle: no congruent sides

7. If point M is the midpoint of JL, classify JKM as equilateral, isosceles, or scalene. Explain your reasoning. 1.3 J K L M 2.0 0.75 Now, classify KML as equilateral, isosceles or scalene.

8. Find the measures of the sides of isosceles triangle ABC. 9x-1 4x+1 5x-0.5 A B C Find the length of each side.

9. Find the measures of the sides of equilateral triangle FGH. Find the length of each side. 2y+5 3y-3 5y-19

10. 4-2 Angles of Triangles

11. Triangle Angle-Sum Theorem: Gives us the relationship among the interior angle measures of any triangle. Triangle Angle-Sum Theorem Theorem 4.1 Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180.

12. Find the measures of each numbered angle. Find the Measures of Each Numbered Angle

13. Exterior Angle Theorem A triangle can have exterior angles formed by one side of the triangle and the extension of an adjacent side. Each exterior angle of a triangle has two remote interior angles that are not adjacent to the exterior angle. Ex. Theorem 4.2 Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

14. Example 3 Find Angle Measures in Right Triangles Find the measures of each numbered angle.