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. 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

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

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. 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 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

10. 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

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.