This document defines and classifies different types of triangles based on their sides and angles. It discusses equilateral, isosceles, scalene, acute, right, obtuse, and equiangular triangles. Key properties are also summarized, such as the triangle sum theorem stating the interior angles sum to 180 degrees, and the exterior angle theorem relating exterior and interior angles.

1. Terms of Endearment Triangles and Angles: 4.1

2. Triangle Figure formed by 3 segments joining 3 non-collinear points

3. Classification by Sides Equilateral Triangle 3 congruent sides Isosceles Triangle At least 2 congruent sides Scalene Triangle No congruent sides

4. Classification by Angles Acute Triangle 3 acute angles Equiangular Triangle 3 congruent angles Right Triangle 1 right angle Obtuse Triangle 1 obtuse angle

5. Vertex Each of the 3 points joining the sides of a triangle

6. Adjacent Sides Two sides sharing a common vertex

7. Right Triangles Legs – Sides that form the right angle Hypotenuse – Side opposite the right angle

8. Isosceles Triangle Leg – the two congruent sides Base – the third side (non-congruent)

9. Interior Angles When the sides of the triangle are extended, the interior angles are the original angles (inside the triangle)

10. Exterior Angles When the sides of a triangle are extended, the exterior angles are the angles adjacent to the interior angles (form a linear pair to the original angles)

11. Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180 degrees

12. Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles

13. Corollary to a theorem Statement easily proven using the theorem

14. Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary