Chapter 2 Lesson 5 Objective To prove and

Chapter 2 Lesson 5 Objective: To prove and apply theorems about angles.

Theorem: the statement that you prove true Theorem 2 -1: Vertical angles are congruent. 2 4 1 3 1 2 and 3 4 Paragraph proof: written as sentences in a paragraph

Example 1: Write a paragraph proof. Given: Prove: 1 and 1 2 are vertical angles 2 Paragraph Proof: By the Angle Addition Postulate, m 1 + m 3 = 180 and m 2 + m 3 = 180. By substitution, m 1 + m 3 = m 2 + m 3. Subtract m 3 from each side. You get m 1 = m 2. 3 1 2

Example 2: Find the value of x. 4 x° (3 x+35)° 4 x = 3 x + 35 Vertical angles are congruent X = 35 Subtract 3 x from each side

Theorem 2 -2: Congruent Supplements Theorem If two angles are supplements of the same angle (or of congruent angles), then two angles are congruent Example 3: Given: Prove: 1 and 2 are supplementary. 3 and 2 are supplementary. 1 3 Proof: By the definition of supplementary angles, m 1 + m 2 = 180 and m 3 + m 2 = 180. By substitution, m 1 + m 2 = m 3 + m 2. Subtract m 2 from each side. You get m 1 = m 3. 2 1 3

Theorem 2 -3: Congruent Complements Theorem If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent. Theorem 2 -4: All right angles are congruent. Theorem 2 -5: If two angles are congruent and supplementary, then each is a right angle.

Homework Page 100 -103 #19 -26; 28 -31; 35 -36; 39 -54