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 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.

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

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.

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

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.

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.

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

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

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

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.

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.