1. Triangles and Angles

2. Triangles
Triangle – 3 segments joining 3 non-collinear
points, called vertices.

3. Classification By Sides
Classification By Angles

4. Classifying Triangles
• In classifying triangles, be as specific as
possible.
Acute,
Scalene
Obtuse,
Isosceles

5. Theorem 4.1 – Triangle Sum Theorem
• The sum of the measures of the interior
angles of a triangle is 180o
.
m A + m∠ B + m C = 180∠ ∠ o

6. To Prove
Given: ΔABC
Prove: m 1 + m 2 + m 3 = 180∠ ∠ ∠ o
Parallel Postulate
2. m 4 + m∠ 2 + m 5 = 180∠ ∠ o
Angle addition postulate, def’n of a straight angle
3. 1 4, 3 5∠ ≅ ∠ ∠ ≅ ∠ Alternate interior angles theorem
4. m 1 = m 4, m 3 = m 5∠ ∠ ∠ ∠ Definition of congruent angles
5. m 1 + m 2 + m 3 = 180∠ ∠ ∠ o
Substitution property of equality

7. Corollary to Triangle Sum Theorem
• A corollary is a statement that readily
follows from a theorem.
The acute angles of a right triangle are
complementary.
m A + m∠ B = 90∠ o

8. Example 1
Find the value of x in the diagram.

9. Theorem 4.2- Exterior Angles Theorem
• The measure of an exterior angle is equal to
the sum of the measures of the 2 non-adjacent
interior angles.
m 1 = m∠ A + m B∠ ∠

10. Example 2
Solve for y in the diagram.

11. Checkpoint: Complete the exercises.

12. Homework
• Exercise 4.1 page 198: 1-47, odd.