1. Chapter 4: Congruent Triangles
Section 4.1: Apply Triangle Sum Properties

2. Section 4.1: Apply Triangle Sum Properties
A triangle with vertices A, B, and C is called “triangle ABC” or “Δ ABC”
A vertex of a triangle is a point that joins two sides of a triangle. The side across from an angle is the opposite side. A c b B C a

3. Section 4.1: Apply Triangle Sum Properties
Triangle Classifications: A triangle can be identified by its sides and by its angles Classifications by sides: (Draw the triangles accurately using rulers!) Scalene: no sides are equal Isosceles: 2 sides are equal Equilateral: 3 sides are equal
Note: an equilateral triangle is also equiangular (all angles are equal)

4. Section 4.1: Apply Triangle Sum Properties
Triangle Classifications by Angles: Acute: all 3 angles are acute Right: has one right angle Obtuse: has one obtuse angle

5. Identify each triangle by its sides and by its angles
Isosceles, Acute
1) 2) 3) 4) 5)
Isosceles, Right
Scalene, Obtuse
Scalene, Right
Equilateral, Equiangular or Acute

6. Section 4.1: Apply Triangle Sum Properties
Triangle Sum Theorem: The sum of the interior angles in a triangle is 180º
Examples:
Find the value of x:
50º
20º xº

7. Section 4.1: Apply Triangle Sum Properties
2) Find the value of x and the angle measurements:
(x + 16)º
(2x)º xº

8. Section 4.1: Apply Triangle Sum Properties
A corollary to a theorem is a statement that can be proved using the theorem. Corollary to the Triangle Sum Theorem: The acute angles of a right triangle are complementary.

9. Section 4.1: Apply Triangle Sum Properties
Interior Angles: Angles inside a triangle (or any polygon) Exterior Angles: Angles that form linear pairs with the interior angles.

10. Section 4.1: Apply Triangle Sum Properties
Exterior Angle Theorem: If one side of a triangle is extended, then the angle formed is equal to the sum of the two remote interior angles
150º
65º
85º
Exterior angle
Remote interior
Remote Interior

11. Section 4.1: Apply Triangle Sum Properties
Find the value of x:
7) Find the value of x and the angle measurements:
(x + 4)º
(2x – 1)º
(6x)º
(3x + 15)º
(2x – 9)º
(2x + 3)º

12. Section 4.1: Apply Triangle Sum Properties
Homework: Pg. 221 #1-10 (all), #14-20 (all)