3.2 โ Use Parallel Lines and Transversals
3.2 โ Use Parallel Lines and Transversals
Identify the angle pairs.
5
1 2
3
7 8
4 6
1.) < 1 ๐๐๐ < 6
Alt. Exterior Angles
2.) < 4 ๐๐๐ < 7
Alt. Interior Angles
3.) < 3 ๐๐๐ < 4
Corresponding Angles
4.) < 2 ๐๐๐ < 7
Consec. Interior Angles
Objective: Students will be able to use parallel lines and specific angle pairs to find angle measures.
AgendaPostulates/Practice
Theorems/Practice
Proving Theorems
Postulate 15 โ Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
1
5
๐
๐
๐
๐ โฅ ๐
< ๐ โ < ๐
Theorem 3.1โ Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
7
3
๐
๐
๐
๐ โฅ ๐
< ๐ โ < ๐
Use the diagram to find ๐ < 3 and ๐ < 5.
๐ < ๐ = ๐๐๐ยฐ (Alt. Int. <โs)๐ < ๐ = ๐๐๐ยฐ (Corr. <โs)
Theorem 3.2โ Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.
4
6
๐
๐
๐
๐ โฅ ๐
< ๐ โ < ๐
Use the diagram to find ๐ < 5 and ๐ < 6.
๐ < ๐ = ๐๐ยฐ (Alt. Int. <โs)๐ < ๐ = ๐๐ยฐ (Alt. Ext.<โs)
Theorem 3.3โ Consecutive Interior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.
2
8
๐
๐
๐ ๐ โฅ ๐
< ๐ ๐๐ง๐ < ๐๐๐ซ๐ ๐ฌ๐ฎ๐ฉ๐ฉ๐ฅ๐๐ฆ๐๐ง๐ญ๐๐ซ๐ฒ
๐ < ๐+๐ < ๐ = ๐๐๐ยฐ
Use the diagram to find ๐ < 3,๐ < 4, and ๐ < 7.
๐ < ๐ = ๐๐๐ยฐ (Alt. Ext. <โs)๐ < ๐ = ๐๐๐ยฐ (Consec. Int.<โs)๐ < ๐ = ๐๐ยฐ (Corr. <โs)
Use the given diagram to find the value of x.
Equation:
115 + ๐ฅ + 5 = 180
120 + ๐ฅ = 180
๐ = ๐๐
115ยฐ4
(๐ฅ + 5)ยฐ
Given the diagram, give a statement that can be made using the following postulate/theorem.
1.) Corresponding Angles Theorem
< 1 โ < 2
2.) Alternate Exterior Angles Theorem
< 3 โ < 8
3.) Consecutive Interior Angles Theorem
๐ < 5 +๐ < 4 = 180ยฐ
4.) Alternate Interior Angles Theorem
< 4 โ < 7
Given: ๐ โฅ ๐
Prove: < 2 โ < 3
Statements Reasons
1. Given1.๐ โฅ ๐
2. < 1 โ < 2
3. < 1 โ < 3
2. Vertical Angle Congruence Theorem
3. Corresponding Angles Postulate
4. < 2 โ < 3 4. Transitive Property
Given: ๐ โฅ ๐
Prove: < 1 โ < 2
Statements Reasons
1. Given1.๐ โฅ ๐
2. < 2 โ < 3
3. < 1 โ < 3
2. Vertical Angle Congruence Theorem
3. Corresponding Angles Postulate
4. < 1 โ < 2 4. Transitive Property
Given: ๐ โฅ ๐
Prove: < 4 and < 5 are supplementary
Statements Reasons 1. Given1.๐ โฅ ๐
2. < 4 โ < 6
4. < 5 and < 6 are supplementary
2. Alternate Interior Angles Theorem
4. Linear Pair Postulate
5. ๐ < 5 +๐ < 6 = 180ยฐ 5. Def. of Supplementary Angles
3. ๐ < 4 = ๐ < 6 3. Def. of Congruent Angles
6. ๐ < 5 +๐ < 4 = 180ยฐ 6. Substitution Property
7.< 4 and < 5 are supplementary 7. Def. of Supplementary Angles