Unit 01 – Lesson 13 – Proving Angle Relationships ESSENTIAL QUESTION How can you prove a mathematical statement? Scholars will… Write proofs involving supplementary and complementary angles. Write proofs involving congruent and right angles.

Angle Addition Postulate (Card #11) If P is in the interior of ∠ RST, then the measure of ∠ RST is equal to the sum of the measures of ∠ RSP and ∠ PST. m ∠ RST = m ∠ RSP + m ∠ PST 2

How do you use Angle Addition Postulate to prove a statement? CONSTRUCTION Using a protractor, a construction worker measures that the angle a beam makes with a ceiling is 42°. What is the measure of the angle the beam makes with the wall?

Linear Pair Postulate (Card #14) If two angles form a linear pair, then they are supplementary.

Complement Theorem (Card #15) If two non-common sides of two adjacent angles form a right angle, then the angles are complementary.

Supplement or Complement? TIME At 4 o’clock, the angle between the hour and minute hands of a clock is 120º. When the second hand bisects the angle between the hour and minute hands, what are the measures of the angles between the minute and second hands and between the second and hour hands?

Properties of Angle Congruence (Card #16)

Congruent Supplements Theorem (Card#17) 3

Congruent Complements Theorem (Card #18)

How do you use Congruent Comp. or Suppl. Theorems to write proofs? Given: Prove:

Vertical Angles Theorem (Card #19) If two angles are vertical angles, then they are congruent.

How do you use Vertical Angles Theorem to prove a statement? If  1 and  2 are vertical angles and m  1 = d – 32 and m  2 = 175 – 2d, find m  1 and m  2. Justify each step.

Right Angles Congruence Theorem (Card #20) All right angles are congruent.

Right Angles and Perpendicular Lines Theorem (Card #21) Perpendicular lines intersect to form 4 right angles.

Perpendicular Lines and Adjacent Angles Theorem (Card #22) Perpendicular lines form congruent adjacent angles.

Congruent & Supplementary Right Angles Theorem (Card #23) If two angles are congruent and supplementary, then each angles is a right angle.

Congruent Linear Pair Theorem (Card #24) If two congruent angles form a linear pair, then they are right angles.