Triangles and Angles

Triangles

Triangle – 3 segments joining 3 non-collinear

points, called vertices.

Classification By Sides

Classification By Angles

Classifying Triangles

• In classifying triangles, be as specific as possible.

Acute,Scalene

Obtuse,Isosceles

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

To Prove

Given: ΔABCProve: 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

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

Example 1

Find the value of x in the diagram.

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 ∠ ∠

Example 2

Solve for y in the diagram.

Checkpoint: Complete the exercises.

Homework

• Exercise 4.1 page 198: 1-47, odd.