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Chapter 2.7 Notes: Prove Angle Pair Relationships Goal: You will use properties of special pairs of angles.

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Theorem 2.3 Right Angles Congruence Theorem: All right angles are congruent. Theorem 2.4 Congruent Supplements Theorem: If two angles are supplementary to the same angle (or to congruent angles), then they are congruent. Theorem 2.5 Congruent Complements Theorem: If two angles are complementary to the same angle (or to congruent angles), then they are congruent.

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Intersecting Lines: When two lines intersect, pairs of vertical angles and linear pairs are formed. Postulate 12 Linear Pair Postulate: If two angles form a linear pair, then they are supplementary. Theorem 2.6 Vertical Angles Congruence Thm: Vertical angles are congruent.

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Ex.1: Use the diagram for (a) – ( c). a. If, find b. If, find c. If, find

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Ex.2: Find x and

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1. If m 1 = 53°, find m 2, m 3, m 4, and m 5. 53° 37° 90°

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2. If m 4 + m 3 = 144°, find m 1, m 2, and m 5. 36° 54° 144°

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3x + 48 = 180 -48 -48 3x = 132 3 x = 44 3. Find the value of x.

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6x – 2 + 7x = 180 +2 +2 13x = 182 13 x = 14 13x – 2 = 180 3. Find the value of x.

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8x = 80 8 x = 10 3. Find the value of x.

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9x + 7 = 5x + 67 -5x -5x. 4x + 7 = 67 4 x = 15 -7 -7 4x = 60 3. Find the value of x.

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4. Find the value of x and y. Then find the measure of each angle. 4y + 17y – 9 = 18021x – 3 + 5x + 1 =180 21y – 9 = 180 21y = 189 y = 9 26x – 2 = 180 26x = 182 x = 7 4(9) = 36° 144° 36° 144°

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4. Find the value of x and y. Then find the measure of each angle. 3x + 7 = 4x – 187y = 5y + 28 7 = x – 18 25 = x y = 14 7(14) = 98° 2y = 28 82° 98° 82° 98°

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Ex.3: Solve for x and y. Find A B (8y – 5) (9x + 12) O (12x – 12) (10y – 15) C D

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Ex.4: Find x and y.

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Ex.5: Find x and y.

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Ex.6: Write a two-column proof. Given: are complements. are complements. Prove:

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