1. - Foldable (you will use this for HW Quiz)
10/26: Apply angle-pair theorems from properties of parallel lines to find missing angle measures.
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- Foldable (you will use this for HW Quiz)
- Today’s Handouts
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Agenda:
HW Quiz & Check
Guided Notes
Guided Practice
Independent Practice
Exit Ticket
Homework
Handout (8 problems)
UNIT 1 RETAKES ON MONDAY!
1st Period

2. We will learn to: - Apply angle-pair theorems from properties of parallel lines to find missing angle measures.

3. parallel measurements When we are given ______________ lines, we can
prove relationships about the ____________________ of
angle-pairs.
measurements

4. corresponding congruent parallel transversal alternate interior
Corresponding Angles Postulate: If two ____parallel____
lines are cut by a ______transversal____, then the ________________ angles are ____________.
Alternate Interior Angles Theorem: If two ________ lines are cut by a _________________, then the __________________ angles are ___________.
corresponding
congruent
parallel
transversal
alternate interior
congruent

5. parallel transversal alternate exterior congruent parallel transversal
Alternate Exterior Angles Theorem: If two ________ lines are cut by a ____________, then the ___________________ angles are ___________.
Consecutive Interior Angles Theorem: If two ___________ lines are cut by a _____________, then ____________________ angles are ________________.
parallel
transversal
alternate exterior
congruent
parallel
transversal
consecutive interior
supplementary

6. 1-8: Justify each statement about the diagram.
∠1 ≅ ∠5
2. ∠4 and ∠7 are supplementary
3. ∠6 ≅ ∠7
4. ∠3 ≅ ∠6
5. m∠5 + m∠7 = 180° ∠4 ≅ ∠5
7. ∠2 &∠5 are supplementary ∠8 ≅ ∠4
Corresponding Angles Postulate
Consecutive Interior Angles Theorem
Vertical Angles
Alternate Exterior Angles Theorem
Linear Pair
Alternate Interior Angles Theorem
Consecutive Interior Angles Theorem
Corresponding Angles Postulate

7. 9. If possible, find m∠1 and m∠2. Justify both answers.
Yes, two lines are parallel
There are MANY different strategies to solve. Let’s go to the whiteboard!

8. No, two lines are NOT parallel
10. If possible, find m∠5 and m∠2 when m∠1 = 144⁰. Justify both answers.
No, two lines are NOT parallel
Yes, form a Linear Pair
m∠1 + m∠2 = 180°
144° + m∠2 = 180°
m∠2 = 36°
Justification: Linear Pair

9. 11. Use the figure on the right to answer the following.
Name the angle-pair created by ∠QST and ∠PST: __________________
Identify the measurement relationship: ______________________________
Write and solve an equation for x.
Linear Pair
Supplementary
m∠QST + m∠PST = 180°

10. 11. Use the figure on the right to answer the following.
Write and solve an equation for x.
Check:
m∠QST + m∠PST = 180°
(3x + 5)° + (6x – 14)° = 180°
9x – 9 = 180°
9x = 189°
x = 21
Justification: Linear Pair
3(21) (21) – 14 = 180°
– 14 = 180°
180° = 180°

11. 11. Use the figure on the right to answer the following.
Name the angle-pair created by ∠RPS and ∠TSP: _________________________________
Identify the measurement relationship: ______________________________
Write and solve an equation for y.
Consecutive Interior Angles
Supplementary
m∠RPS + m∠TSP = 180°

12. 11. Use the figure on the right to answer the following.
Write and solve an equation for y.
Check:
m∠RPS + m∠TSP = 180°
(y + 8)° + 126° = 180°
y ° = 180°
y = 46
Justification: Consecutive Interior Angles Theorem
(46) = 180°
180° = 180°

13. Congruent _______ = _______
12. If m∠1 = (6z)⁰ and m∠4 = (4z + 7)⁰, find the value of z and justify, if possible.
Yes, the two lines are ||
Alternate Interior Angles
Congruent
m∠ m∠4
_______ = _______
6z = 4z + 7
2z = 7
z = 3.5
Justification: Alternate Interior Angles Theorem

14. Independent Practice Answers
m∠4 = 115° (Vertical Angles)
x = 80 (Consecutive Interior Angles Theorem)
2. Not possible – lines are not parallel
3. m∠1 = 90° (Consecutive Interior Angles Theorem)
m∠3 = 65° (Linear Pair with 115°)
m∠2 = 65° (Corresponding Angles with 115°)
4. a) m∠2 = 115° (Corresponding Angles with 115°)
b) m∠1 = 115° (Alternate Interior Angles with 115°)
5. x = 12 (Consecutive Interior Angles)
y = 10 (Consecutive Interior Angles)