The document discusses different types of triangles classified by their sides or angles. It can classify triangles as scalene, isosceles, or equilateral based on their side lengths. It also defines acute, obtuse, and right triangles based on their angle measures. The document then provides proofs that the sum of the interior angles of any triangle is 180 degrees and that an exterior angle of a triangle is equal to the sum of the two remote interior angles.

1. GEOMETRY Triangles

2. We can classify triangles by their sides: Scalene – no sides are the same length

3. We can classify triangles by their sides: Isosceles – two sides are the same length (Base angles are also equal)

4. We can classify triangles by their sides: Equilateral – all sides are the same length (All angles are also equal and 60 °)

5. We can classify triangles by their angles: Acute angles – all angles are acute

6. We can classify triangles by their angles: Obtuse angles – one angle is obtuse

7. We can classify triangles by their angles: Right angled – one angle is a right angle

8. PROOF – Angle Sum of a Triangle Construction: Draw a line DE parallel to AC. D E ﮮ ACB = ﮮ CBE = z ° (Alternate angles on AC║DE) z ° ﮮ BAC = ﮮ ABD = y ° (Alternate angles on AC║DE) y ° ﮮ DBA + ﮮ ABC + ﮮ EBC = 180 ° y° + x° + z° = 180° (Angles on a straight line add to 180 ° ) Therefore ﮮ BCA + ﮮ ABC + ﮮ BAC = 180 °

9. PROOF – Exterior Angle of a Triangle Construction: Draw CE parallel to AB. ﮮ BAC = ﮮ ECD = y ° (Corresponding angles on AC║DE) ﮮ ABC = ﮮ BCE = x ° (Alternate angles on AC║DE) ﮮ BCD = ﮮ ABC + ﮮ BAC z° = x° + y° D E z °