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
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∠ ∠
