1. Triangles and Their Angles Geometry – Section 4.1

2. Definition A triangle is formed by three segments joining noncollinear points. We have different classifications of triangles based on their sides and angles.

3. Classes of Triangles Equilateral triangle (3 congruent sides) Isosceles triangle (at least 2 congruent sides)

4. Classes of Triangles Scalene triangle (no congruent sides)

5. Classes of Triangles  Acute triangle (3 acute angles)  Right triangle (1 right angle)

6. Classes of Triangles  Obtuse triangle (1 obtuse angle)  Equiangular triangle (3 congruent angles)

7. Other Definitions In a triangle:  point where sides meet: vertex  2 sides sharing a vertex: adjacent sides

8. Other Definitions A side is opposite an angle if it is the side of the triangle that does not form the angle.

9. Other Definitions In a right triangle, the side opposite the right angle is called the hypotenuse. The other two sides are called the legs.

10. Other Definitions In a right triangle, the side opposite the right angle is called the hypotenuse. The other two sides are called the legs.

11. Other Definitions In an isosceles triangle, the sides that are congruent are the legs. The other side is called the base. 

12. Assignment p.198-199: 6-8, 10-28

13. More with Triangles Geometry – Section 4.1

14. Interior and Exterior Angles Interior angles are the three angles inside a triangle.

15. Interior and Exterior Angles If a line or ray is extended from one of the vertices, the angle formed is an exterior angle.

16. Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180º.

17. Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the other 2 interior angles.

18. Example Find the measure of the numbered angles.

19. Example Find the measure of the numbered angles.

20. Example Find the measure of each angle in ABC.

21. Assignment p.199: 31-39