4.1 triangles and angles
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Transcript of 4.1 triangles and angles
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.