2-8 Proving Angle Relationships day 2

•Use the Angle Addition Postulate to find the measure of angles.

• Write proofs involving supplementary and complementary angles.

• Write proofs involving congruent and right angles.

The properties of algebra that applied to the congruence of segments and the equality of their measures also hold true for the congruence of angles and the equality of their measures.

In your book on page 153

Page 153 in your book

Page 154 in your book

Proofs Using Congruent Comp. or Suppl. Theorems

Given:

Prove:

1. Given1. m3 + m1 = 180;1 and 4 form a linear pair.

4. s suppl. to same are .

4. 3 4

Proof:Statements Reasons

2. Linear pairs are supplementary.

2. 1 and 4 aresupplementary.

3. Definition of supplementary angles

3. 3 and 1 are supplementary.

Given:

Prove:

In the figure, NYR and RYA form a linear pair,AXY and AXZ form a linear pair, and RYA andAXZ are congruent. Prove that NYR and AXY are congruent.

Statements Reasons

1. Given1. NYR and RYA, AXY and AXZ form linear pairs.

2. If two s form a linear pair, then they are suppl. s.

2. NYR and RYA are supplementary. AXY and AXZ are supplementary.

3. Given3. RYA AXZ4. NYR AXY 4. ____________ ?s supp. to the same

or to s are .

Remember that Vertical Angles are two nonadjacent angles formed by intersecting lines.

If 1 and 2 are vertical angles and m1 = d – 32 and m2 = 175 – 2d, find m1 and m2. Justify each step.

1. Given1. 1 and 2 are vertical s.2. Vertical Angles Theorem3. Definition of cong. angles4. Substitution

2. 1 23. m1 = m24. d – 32 = 175 – 2d

Statements Reasons

5. Addition Property5. 3d – 32 = 1756. Addition Property7. Division Property7. d = 69

Answer: m1 = 37 and m2 = 37

m1 = d – 32 m2 = 175 – 2d

= 69 – 32 or 37 = 175 – 2(69) or 37

6. 3d = 207

A.

B.

C.

D. 𝑚∠𝐴=3𝑏−23 𝑚∠𝑍=152−4𝑏

2-8 Assignmentp. 156, Name the theorems used in 8 to 13 from yesterday. Then work 6 & 7