http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines
Prove:l||m
TABLE3.3:
Statement Reason
1.landmand transversalt^63 ∼=^66 Given
2.^63 ∼=^62 Vertical Angles Theorem
3.^62 ∼=^66 Transitive PoC
4.l||m Converse of the Corresponding Angles Postulate
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CK-12 Foundation: Chapter3AlternateInteriorAnglesB
Vocabulary
Alternate Interior Anglesare two angles that are on theinterior oflandm, but on opposite sides of the transversal.
Guided Practice
- Isl||m?
- What doesxhave to be to makea||b?
- List the pairs of alternate interior angles:
Answers:
- First, findm^6 1. We know its linear pair is 109◦. By the Linear Pair Postulate, these two angles add up to 180◦, so
m^61 = 180 ◦− 109 ◦= 71 ◦. This means thatl||m, by the Converse of the Corresponding Angles Postulate. - Because these are alternate interior angles, they must be equal fora||b. Set the expressions equal to each other
and solve.
3 x+ 16 ◦= 5 x− 54 ◦
70 ◦= 2 x
35 ◦=x To makea||b,x= 35 ◦.
- Alternate Interior Angles:^6 4 and^6 5,^6 3 and^6 6.
Practice
- Is the angle pair^6 6 and^6 3 congruent, supplementary or neither?
- Give two examples of alternate interior angles in the diagram: