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3.2: Properties of Parallel Lines

Today’s Objectives

Understand theorems about parallel lines

Use properties of parallel lines to find angle measurements

Corresponding Angles Postulate Postulate 3-1: If a transversal intersects two

parallel lines, then corresponding angles are congruent

1 2

3 4

5 6

7 8

Indicates Parallel

Alternate Interior Angles Theorem Theorem 3-1: if a transversal intersects two

parallel lines, then alternate interior angles are congruent

1 2

3 4

5 6

7 8

Consecutive Interior Angles Theorem Theorem 3-2: if a transversal intersects two

parallel lines, then consecutive (same-side) interior angles are supplementary

1 2

3 4

5 6

7 8

Alternate Exterior Angles Theorem Theorem 3-3: if a transversal intersects two

parallel lines, then alternate exterior angles are congruent

1 2

3 4

5 6

7 8

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Angles and Parallel Lines

If two parallel lines are cut by a transversal, then the following pairs of angles are CONGRUENT.

Corresponding angles Alternate interior angles Alternate exterior angles

If two parallel lines are cut by a transversal, then the following pairs of angles are SUPPLEMENTARY.

Consecutive interior angles Consecutive exterior angles

Example

Fill in all of the angle measurements if m<2 = 68.

𝑚<1=112

𝑚<3=68

𝑚<4=112

𝑚<5=112

𝑚<7=68

𝑚<6=68

𝑚<8=112

1 2

3 4

5 6

7 8

Example

𝐼𝑓 𝑚∠5=𝑥−50 ,𝑎𝑛𝑑𝑚∠3=𝑥 , h𝑤 𝑎𝑡 𝑖𝑠𝑚∠4 ?𝑚∠5+𝑚∠3=180

𝑥−50+𝑥=180

2 𝑥−50=180

2 𝑥=230

𝑥=115

𝑚∠4=𝑚∠ 5=𝑥−50

𝑚∠4=115−50=65

Example

Solve for x.

17 𝑥+14+4 𝑥−2=180

21 𝑥+12=180

21 𝑥=168

𝑥=8

17(8) + 14=150

4(8) – 2 =30

Take Home

Special angles have special relationships Alternate Congruent

Consecutive (Same-Side) Supplementary

Corresponding Congruent