CK-12 Geometry Concepts

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

Watch this video for help with the Examples above.

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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

1. Isl||m?


2. What doesxhave to be to makea||b?


3. List the pairs of alternate interior angles:

Answers:

1. 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.


2. 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 ◦.

3. Alternate Interior Angles:^6 4 and^6 5,^6 3 and^6 6.

Practice

1. Is the angle pair^6 6 and^6 3 congruent, supplementary or neither?


2. Give two examples of alternate interior angles in the diagram: