1. Geometry : Triangles By: Mr. Mellas

2. Triangles Classified by the angles they contain. Three types -Acute, Obtuse, and Right Acute - All acute angles Obtuse - One obtuse angle Right - One right angle

3. Acute Triangles Example Notice that all angles are less than 90°. Therefore, this is an acute triangle. 60°

4. Obtuse Triangles Example 30 ° 130°20° This is an obtuse triangle because there is one angle that is greater than 90°. Obtuse Angle

5. Right Triangle Example Right Angle This is a right triangle because there is one angle that is 90°

6. Measurement You need to remember that in every triangle, all angles have to equal 180° when the sum of the angles is found. 60° 60 + 60 + 60 = 180

7. Finding Angle Measurements You need to remember that all angles total 180°. 50° x Notice that you have 2 angles given already. - Find their sum, then subtract from 180 1. 90 + 50 = 140 2. 180 – 140 = 40 3. Angle x = 40°

8. Other Examples Solve for x. 85° 46° x X = 49° 29° x 55° X = 96°

9. Remembering Angle Relationships  Remember vertical angle rules 55° x 50° Solve for x A B C D E Since angle DCE = 90° then angle CED = 35°

10. Remembering Angle Relationships Remember supplementary angle rules 75° x L M N P Since angle LPM = 75° then angle MPN = 105° because they are supplementary.

11. Your Turn Solve for the missing angles 80˚ 30˚ x Y 75˚ Z Angle X= 70˚ Angle Y = 70˚ Angle Z = 35˚