# Proving angles congruent. To prove a theorem, a “Given” list shows you what you know from the hypothesis of the theorem. You will prove the conclusion.

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Proving angles congruent

To prove a theorem, a “Given” list shows you what you know from the hypothesis of the theorem. You will prove the conclusion of the theorem. what you know:Given what you must show: Prove Diagram shows what you know. 40

Using the Vertical Angles Theorem: Find the value of x. (4x) 0 (3x + 35) 0 4x = 3x + 35 - 3x -3x x = 35 4(35) = 3(35) + 35 = 140 Find the measure of the labeled pair.

Using the Vertical Angles Theorem: Find the value of x. (4x) 0 (3x + 35) 0 x + 140 = 180 - 140 -140 x = 40 Find the measure of the other pair. (x) 0

Theorem 2 – 2: Congruent Supplements Theorem; If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.

Proving Theorem 2 – 2: Given: < 1 and < 2 are supplementary. < 3 and < 2 are supplementary. Prove: < 1 < 3 By 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 both sides m < 1 = m < 3 ~ = 1 2 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.

Here comes the assignment!! page 283 (1-13 all) Here comes the assignment!! page 283 (1-13 all)

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