1. Chapter 4 Section 4.1 – Part 1
Triangles and Angles

2. Warm-Up

3. Definition of a Triangle
Triangle: () A figure formed by three segments joining three non-collinear points

4. Parts of a Triangle
Vertex
Interior Angle
Side
Exterior Angle

5. Classifying Triangles by Sides
Equilateral 
3 congruent Sides
Isosceles 
At least 2 congruent Sides
Scalene 
No Sides congruent

6. Special Vocabulary in Isosceles Triangles
Legs A B C
ABC is isosceles
are the legs
Two Congruent Sides
is the base
The “other” side
Base

7. Classifying Triangles by Angles
Equiangular 
3 congruent Angles
Acute 
All Angles are Acute
Right 
One Right Angle
Obtuse 
One obtuse Angle

8. Special Vocabulary in Right TrianglesD E F
DEF is a right 
are the legs
Two Perpendicular Sides
Legs
is the Hypotenuse
The side opposite the right angle
Hypotenuse

9. Hyp
Leg
Base

10. Classify the Triangle by Its Angles and Sides
Acute/Isosceles
Right/Scalene
Equilateral/Equiangular
Obtuse/Scalene
Right/Scalene
Obtuse/Isosceles

11. Classify the Sentence With Always, Sometimes, or Never
An equilateral triangle is _____ an isosceles triangle
Always
An isosceles triangle is _____ an equilateral triangle
Sometimes
A right triangle is _____ an acute triangle
Never
An exterior angle of a triangle is _____ acute

12. Triangle Sum Theorem Inductive reasoning
Triangle Sum Theorem: The sum of the measures of the angles of a triangle is 180°
mA + mB + mC = 180°

13. Find the Measure of the Numbered Angle
Triangle Sum Theorem
m = 180
m = 180
m1 = 48

14. Corollary to the Triangle Sum Theorem
Corollary: A statement that can be easily proven using the theorem.
Inductive reasoning
Corollary to the triangle sum theorem: the acute angles of a right triangle are complementary.
mA + mC = 90

15. Find the Measure of the Numbered Angle
Corollary Triangle Sum Theorem
m = 90
m1 = 37
m = 90
m2 = 57

16. Exterior Angle Theorem
Inductive Reasoning
Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles
mA + mB = mBCD

17. Find the Measure of the Numbered Angle
Exterior Angle Theorem
m = 102
m1 = 34
Linear Pair Postulate
m = 180
m2 = 78