1. 3.2 – Use Parallel Lines and Transversals
Geometry Chapter 3
3.2 – Use Parallel Lines and Transversals

2. Warm-Up 1.) <1 𝑎𝑛𝑑<6 Alt. Exterior Angles 2.) <4 𝑎𝑛𝑑<7
Identify the angle pairs.
1.) <1 𝑎𝑛𝑑<6
Alt. Exterior Angles
2.) <4 𝑎𝑛𝑑<7
Alt. Interior Angles
3.) <3 𝑎𝑛𝑑<4
Corresponding Angles
4.) <2 𝑎𝑛𝑑<7
Consec. Interior Angles 5 1 2 3 7 8 4 6

3. Use Parallel Lines and Transversals
Objective: Students will be able to use parallel lines and specific angle pairs to find angle measures.
Agenda
Postulates/Practice
Theorems/Practice
Proving Theorems

4. For the Postulates List
Postulate 15 – Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 5 𝒎 𝒏 𝒕
𝒎 ∥𝒏
<𝟏≅ <𝟓

5. For the Theorems List 𝒎 ∥𝒏 <𝟑≅ <𝟕
Theorem 3.1– Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 7 3 𝒎 𝒏 𝒕
𝒎 ∥𝒏
<𝟑≅ <𝟕

6. Practice – Postulate 15/Thm 3-1
Use the diagram to find 𝑚<3 and 𝑚<5.
𝒎<𝟓=𝟏𝟒𝟎° (Alt. Int. <‘s)
𝒎<𝟑=𝟏𝟒𝟎° (Corr. <‘s)

7. For the Theorems List 𝒎 ∥𝒏 <𝟒≅ <𝟔
Theorem 3.2– Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. 4 6 𝒎 𝒏 𝒕
𝒎 ∥𝒏
<𝟒≅ <𝟔

8. Practice – Thm 3-2 𝒎<𝟓=𝟖𝟕° (Alt. Int. <‘s)
Use the diagram to find 𝑚<5 and 𝑚<6.
𝒎<𝟓=𝟖𝟕° (Alt. Int. <‘s)
𝒎<𝟔=𝟗𝟑° (Alt. Ext. <‘s)

9. For the Theorems List 𝒎 ∥𝒏 <𝟐 𝐚𝐧𝐝 <𝟖 𝐚𝐫𝐞 𝐬𝐮𝐩𝐩𝐥𝐞𝐦𝐞𝐧𝐭𝐚𝐫𝐲
Theorem 3.3– Consecutive Interior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. 2 8 𝒎 𝒏 𝒕
𝒎 ∥𝒏
<𝟐 𝐚𝐧𝐝 <𝟖
𝐚𝐫𝐞 𝐬𝐮𝐩𝐩𝐥𝐞𝐦𝐞𝐧𝐭𝐚𝐫𝐲
𝒎<𝟐+𝒎<𝟖=𝟏𝟖𝟎°

10. Practice – Thm 3-2 𝒎<𝟑=𝟏𝟑𝟓° (Alt. Ext. <‘s)
Use the diagram to find 𝑚<3, 𝑚<4, and 𝑚<7.
𝒎<𝟑=𝟏𝟑𝟓° (Alt. Ext. <‘s)
𝒎<𝟒=𝟏𝟑𝟓° (Consec. Int. <‘s)
𝒎<𝟕=𝟒𝟓° (Corr. <‘s)

11. Example Equation: 115+𝑥+5=180 120+𝑥=180 𝒙=𝟔𝟎 115° 4 (𝑥+5)°
Use the given diagram to find the value of x.
Equation:
115+𝑥+5=180
120+𝑥=180
𝒙=𝟔𝟎
115° 4
(𝑥+5)°

12. Exit Ticket. 1.) Corresponding Angles Theorem <1≅ <2
Given the diagram, give a statement that can be made using the following postulate/theorem.
1.) Corresponding Angles Theorem
<1≅ <2
2.) Alternate Exterior Angles Theorem
<3≅ <8
3.) Consecutive Interior Angles Theorem
𝑚<5+𝑚<4=180°
4.) Alternate Interior Angles Theorem
<4≅ <7

13. Proving Theorem 3-1 Given: 𝑚∥𝑛 Prove: <2≅ <3 Statements Reasons
1.𝑚∥𝑛
1. Given
2. <1≅ <2
2. Vertical Angle Congruence Theorem
3. <1≅ <3
3. Corresponding Angles Postulate
4. <2≅ <3
4. Transitive Property

14. Proving Theorem 3-2 Given: 𝑚∥𝑛 Prove: <1≅ <2 Statements Reasons
1.𝑚∥𝑛
1. Given
2. <2≅ <3
2. Vertical Angle Congruence Theorem
3. <1≅ <3
3. Corresponding Angles Postulate
4. <1≅ <2
4. Transitive Property

15. Proving Theorem 3-3 Given: 𝑚∥𝑛 Prove: <4 and<5 are supplementary
Statements Reasons
1.𝑚∥𝑛
1. Given
2. <4≅ <6
2. Alternate Interior Angles Theorem
3. 𝑚<4=𝑚<6
3. Def. of Congruent Angles
4. <5 and<6 are supplementary
4. Linear Pair Postulate
5. 𝑚<5+𝑚<6=180°
5. Def. of Supplementary Angles
6. 𝑚<5+𝑚<4=180°
6. Substitution Property
7.<4 and<5 are supplementary
7. Def. of Supplementary Angles