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3) Solve for y. Given: AC=21. State the reason that justifies each step.

BELLWORK. 3) Solve for y. Given: AC=21. State the reason that justifies each step. 2y. 3y-9. AB + BC = AC 2y + (3y-9) = 21 5y - 9 = 21 5y = 30 y= 6. Segment addition postulate Substitution property Simplify Addition property of equality Division property of equality. A. B. C.

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3) Solve for y. Given: AC=21. State the reason that justifies each step.

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  1. BELLWORK 3) Solve for y. Given: AC=21. State the reason that justifies each step. 2y 3y-9 • AB + BC = AC • 2y + (3y-9) = 21 • 5y - 9 = 21 • 5y = 30 • y= 6 • Segment addition postulate • Substitution property • Simplify • Addition property of equality • Division property of equality A B C

  2. 2-5 Proving Angles Congruent Geometry

  3. 5 6 Adjacent Angles Adjacent angles- two coplanar angles with a common side, a common vertex, and no common interior points.

  4. Vertical Angles and Linear Pairs 5 6 Two angles are vertical angles if their sides form two pairs of opposite rays. Two adjacent angles are a linear pair if their noncommon sides are opposite rays. 1 2 4 3 1 and 3 are vertical angles. 5 and 6 are a linear pair. 2 and 4 are vertical angles.

  5. Complementary and Supplementary Angles 4 1 2 3 Complementary angles – Two angles whose sum is 90˚. *Complementary angles can be adjacent or nonadjacent. complementary adjacent complementary nonadjacent

  6. Complementary and Supplementary Angles 7 8 5 6 Supplementary angles- Two Angles whose measures have a sum of 180. * Supplementary angles can be adjacent or non adjacent supplementary adjacent supplementary nonadjacent

  7. Identifying Vertical Angles and Linear Pairs 1 2 3 4 Answer the questions using the diagram. Are 2 and 3 a linear pair? SOLUTION The angles are adjacent but their noncommon sides are not opposite rays. No.

  8. Identifying Vertical Angles and Linear Pairs 1 2 3 4 Answer the questions using the diagram. Are 2 and 3 a linear pair? Are 3 and 4 a linear pair? Supplementary? SOLUTION The angles are adjacent but their noncommon sides are not opposite rays. No. Yes. The angles are adjacent and their noncommon sides are opposite rays.

  9. Identifying Vertical Angles and Linear Pairs 1 2 3 4 Answer the questions using the diagram. Are 2 and 3 a linear pair? Are 3 and 4 a linear pair? Are 1 and 3 vertical angles? SOLUTION The angles are adjacent but their noncommon sides are not opposite rays. No. Yes. The angles are adjacent and their noncommon sides are opposite rays. No. The sides of the angles do not form two pairs of opposite rays.

  10. Identifying Vertical Angles and Linear Pairs 1 2 3 4 Answer the questions using the diagram. Are 2 and 3 a linear pair? Are 3 and 4 a linear pair? Are 1 and 3 vertical angles? Are 2 and 4 vertical angles? SOLUTION The angles are adjacent but their noncommon sides are not opposite rays. No. Yes. The angles are adjacent and their noncommon sides are opposite rays. No. The sides of the angles do not form two pairs of opposite rays. The sides of the angles do not form two pairs of opposite rays. No.

  11. Congruent Supplements Theorem • Theorem 2-2: Congruent Supplements. If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.

  12. Congruent Complements Theorem • Theorem 2-3: If two angles are complementary to the same angle (or 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

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