Download 3-2 Angles Formed by Parallel Lines and Transversals

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SUBJECT MATTER: PROPERTIES OF PARALLEL LINES
Pacing:
Objective:
To prove theorems about parallel lines
2 days
To use properties of parallel lines to find angle
measures
Standards
G-2.2 Apply properties of parallel lines, intersecting lines, and parallel lines cut by a transversal to
solve problems.
G-1.1 Demonstrate an understanding of the axiomatic structure of geometry by using undefined
terms, definitions, postulates, theorems, and corollaries.
Warm Up:
HSAP Review
The equation C = $0.05m + 4.95 represents the cost (C) of a long distance telephone call m minutes. What does the rate
of change represent in this situation?
a. the initial charge for a call
b. the cost of a long distance call
c. the number of minutes of the call
d. the cost per
Postulate 3 - 2 - 1 Corresponding Angle Postulate
POSTULATE
HYPOTHESIS
If two parallel lines are cut by a transversal,
then the pairs of corresponding angles are
congruent.
CONCLUSION
∠1 ≅ ∠3
∠2 ≅ ∠4
∠5 ≅ ∠7
∠6 ≅ ∠8
Example 1 Using the Corresponding Angles Postulate
Find each angle measure.
A. 𝑚∠𝐴𝐵𝐶
B. 𝑚∠𝐷𝐸𝐹
C. 𝑚∠𝑄𝑅𝑆
Theorems: Parallel Lines and Angle Pairs
THEOREM
3 -2 -2
HYPOTHESIS
CONCLUSION
Alternate Interior Angles
Theorem
∠1 ≅ ∠3
If two parallel lines are cut by a
transversal, then the pairs of
alternate interior angles are
congruent
3 -2 -3
∠2 ≅ ∠4
Alternate Exterior Angles
Theorem
∠5 ≅ ∠7
If two parallel lines are cut by a
transversal, then the pairs of
alternate exterior angles are
congruent
3 -2 -4
∠6 ≅ ∠8
Same-Side Interior Angles
Theorem
𝑚∠1 + 𝑚∠4 = 1800
If two parallel lines are cut by a
transversal, then the pairs of sameside interior angles are
supplementary
𝑚∠2 + 𝑚∠3 = 1800
Example 2 Finding Angle Measures
Find each angle measure.
A. 𝑚∠𝐸𝐷𝐹
B. 𝑚∠𝑇𝑈𝑆
C. 𝑚∠𝐴𝐵𝐷
Example 3 Finding Angle Measures
In the figure, 𝑛
⃡∥𝑚
⃡ , 𝑚∠4 = 50 and 𝑚∠16 = 80. Find the measure of each angle.
A. ∠8 = _______________
B. ∠5 = _______________
C. ∠2 = _______________
D. ∠1 = _______________
E. ∠6 = _______________
F. ∠3 = _______________
G. ∠12 = _______________
H. ∠13 = _______________
I. ∠9 = _______________
J. ∠10 = _______________
K. ∠15 = _______________
L. ∠17 = _______________
Classwork
Name: ____________________________________
Period: __________________ Date: _______________
Find each angle measure.
1. 𝑚∠𝐽𝐾𝐿
5. 𝑚∠𝐸𝐶𝐹
6. 𝑚∠𝐷𝐶𝐸
2. 𝑚∠𝐵𝐸𝐹
7. 𝑚∠𝐸𝐷𝐺
3. 𝑚∠1
4. 𝑚∠𝐶𝐵𝑌
8. 𝑚∠𝐵𝐷𝐺
In the figure at the right 𝑚 ∥ 𝑛, 𝑚∠4 = 590 and 𝑚∠15 = 770. Find the measure of each angle.
9. ∠3 =
10. ∠5 =
11. ∠13 =
12. ∠9 =
13. ∠15 =
14. ∠7 =
15. ∠8 =
16. ∠12 =
17. ∠16 =
18. ∠17 =
HW: Do # 7 - 17 on page 153
Name: ____________________________________
Period: __________________ Date: _______________
Find each angle measure.
1. 𝑚∠𝐾𝐿𝑀
2. 𝑚∠𝑉𝑌𝑋
3. 𝑚∠𝐴𝐵𝐶
4. 𝑚∠𝐸𝐹𝐺
5. 𝑚∠𝑃𝑄𝑅
6. 𝑚∠𝑆𝑇𝑈
In the figure at the right, 𝑝
⃡∥ 𝑞
⃡, 𝑚∠1 = 107 and 𝑚∠11 = 48. Find the measure of each angle.
7. ∠3 =
8. ∠5 =
9. ∠13 =
10. ∠9 =
11. ∠15 =
12. ∠7 =
13. ∠8 =
14. ∠12 =
15. ∠16 =