Presentation on theme: "Proving Angle Relationships"— Presentation transcript:
1 Proving Angle Relationships Postulate 2.10 – Protractor PostulateGiven 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 PostulateIf R is in the interior of PQS, then mPQR + mRQS = m PQS.If mPQR + mRQS = mPQS, then R is in the interior of PQS.
3 and is a right angle, find QUILTING The diagram below shows one square for a particular quilt pattern. Ifandis a right angle, findAnswer: 50Example 8-1c
4 Proving Angle Relationships Theorem 2.3 – Supplement TheoremIf two angles form a linear pair, then they are supplementary angles.Theorem 2.4 – Complement TheoremIf the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles.
5 are complementary angles and . and If find Answer: 28Example 8-2b
6 Proving Angle Relationships Theorem 2.5 – Angle Congruence TheoremCongruence of angles is reflexive, symmetric, and transitive.Reflexive: 1 1Symmetric: If 1 2, then 2 1.Transitive: If 1 2 and 2 3, then 1 3.
7 Proving Angle Relationships Theorem 2.6Angles supplementary to the same angle or to congruent angles are congruent.Theorem 2.7Angles complementary to the same angle or to congruent angles are congruent.Vertical Angles TheoremIf two angles are vertical angles, then they are congruent.
8 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 AXY are congruent.Example 8-3c
9 2. If two s form a linear pair, then they are suppl. s. Proof:Statements Reasons1. Given2. If two s form a linear pair, then they are suppl. s.3. Given220.127.116.11.linear pairs.Example 8-3d
10 If and are vertical angles and and find andIf and are vertical angles andandAnswer: mA = 52; mZ = 52Example 8-4c
11 Proving Angle Relationships Theorem 2.9Perpendicular lines intersect to form four right angles.Theorem 2.10All right angles are congruent.Theorem 2.11Perpendicular lines form congruent adjacent angles.
12 Proving Angle Relationships Theorem 2.12If two angles are congruent and supplementary, then each angle is a right angle.Theorem 2.13If two congruent angles form a linear pair, then they are right angles.