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Proving Angle Relationships

Proving Angle Relationships. Postulate 2.10 – Protractor Postulate Given ray AB and a number r between 0 and 180, there is exactly one ray with endpoint A extending on either side of ray AB, such that the measure of the angle formed is r. Proving Angle Relationships.

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Proving Angle Relationships

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  1. Proving Angle Relationships Postulate 2.10 – Protractor Postulate • Given ray AB and a number r between 0 and 180, there is exactly one ray with endpoint A extending on either side of ray AB, such that the measure of the angle formed is r.

  2. Proving Angle Relationships Postulate 2.11 – Angle Addition Postulate • If R is in the interior of PQS, then mPQR + mRQS = m PQS. • If mPQR + mRQS = mPQS, then R is in the interior of PQS.

  3. QUILTING The diagram below shows one square for a particular quilt pattern. If and is a right angle, find Example 8-1c Answer: 50

  4. Proving Angle Relationships Theorem 2.3 – Supplement Theorem • If two angles form a linear pair, then they are supplementary angles. Theorem 2.4 – Complement Theorem • If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles.

  5. If are complementary angles and . and find Example 8-2b Answer: 28

  6. Proving Angle Relationships Theorem 2.5 – Angle Congruence Theorem Congruence of angles is reflexive, symmetric, and transitive. Reflexive: 1 1 Symmetric: If 1  2, then 2  1. Transitive: If 1  2 and 2  3, then 1  3.

  7. Proving Angle Relationships Theorem 2.6 • Angles supplementary to the same angle or to congruent angles are congruent. Theorem 2.7 • Angles complementary to the same angle or to congruent angles are congruent. Vertical Angles Theorem • If two angles are vertical angles, then they are congruent.

  8. Example 8-3c In the figure, NYR and RYA form a linear pair,AXY and AXZ form a linear pair, and RYA and AXZ are congruent. Prove that RYN and AXYare congruent.

  9. Proof: Statements Reasons 1. 1. Given linear pairs. 2. 2. If two s form a linear pair, then they are suppl. s. 3. 3. Given 4. 4. Example 8-3d

  10. If and are vertical angles and and find and Example 8-4c Answer: mA= 52; mZ= 52

  11. Proving Angle Relationships Theorem 2.9 • Perpendicular lines intersect to form four right angles. Theorem 2.10 • All right angles are congruent. Theorem 2.11 • Perpendicular lines form congruent adjacent angles.

  12. Proving Angle Relationships Theorem 2.12 • If two angles are congruent and supplementary, then each angle is a right angle. Theorem 2.13 • If two congruent angles form a linear pair, then they are right angles.

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