Get Ready for Chapter 3Get Ready for Chapter 3

P.125 1-11P.125 1-11

3-1 PARALLELS3-1 PARALLELS

I. I. PARALLEL LINESPARALLEL LINES

II. INTERSECTING LINESII. INTERSECTING LINES

III. SKEW LINESIII. SKEW LINES

IV. TRANSVERSALSIV. TRANSVERSALS

EXAMPLESEXAMPLES

1. Name the plane parallel to plane AEF

2. Which segment is skew to GH?2. Which segment is skew to GH?

3. How many segments intersect 3. How many segments intersect AM? AM?

4.  Name a pair of consecutive 4.  Name a pair of consecutive interior angles interior angles

5.  Which statement is true 5.  Which statement is true about skew lines? about skew lines? A.They intersectA.They intersectB.They lie in the same plane. B.They lie in the same plane. C.They are perpendicularC.They are perpendicularD.They do not intersect.D.They do not intersect.

6. Identify:6. Identify: a.a. Name all planes Name all planes

that are parallel to that are parallel to plane plane ABCABC..

b.b. Name all segments Name all segments that intersect AB.that intersect AB.

c.c. Name all segments Name all segments that are parallel to KG.that are parallel to KG.

d.d. Name all segments Name all segments that are skew to TK.that are skew to TK.

7. Texas is the leading producer of livestock 7. Texas is the leading producer of livestock in the United States. A diagram of a feed lot in the United States. A diagram of a feed lot on a farm is shown below. Identify the sets of on a farm is shown below. Identify the sets of lines to which each given line is a lines to which each given line is a transversal.transversal.

a.a. line line kk b.b. line line ss c.c. line line pp d.d. line line mm

8. 8. Refer to the figure below. Identify each pair Refer to the figure below. Identify each pair of angles as of angles as alternate interioralternate interior, , alternate alternate

exteriorexterior, , correspondingcorresponding, or , or consecutive interiorconsecutive interior angles.angles.

a.a. 2 and 2 and 1010 b.b. 9 and 9 and 77 c.c. 1 and 1 and 77 d.d. 12 and 12 and 88 e.e. 11 and 11 and 88 f.f. 4 and 4 and 1212

ClassworkClasswork

P. 128 1-21P. 128 1-21

3-2

ANGLES

Corresponding angles

1

2

1 2

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

Alternate Interior

3

4

3 4

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Consecutive Interior

56

m 5 + m 6 = 180°

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

Alternate Exterior

7

8

7 8

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

Perpendicular transversal

j k

If a transversal is perpendicular to one of two parallellines, then it is perpendicular to the other.

Examples1. If < 3 = 108, find all other angles.

1 2 3 4

5 6 7 8

A B

C D

2. Use properties ofparallel lines to findthe value of x.

SOLUTION

Corresponding Angles Postulatem 4 = 125°

Linear Pair Postulatem 4 + (x + 15)° = 180°

Substitute.125° + (x + 15)° = 180°

Subtract.x = 40°

3. Find the measure of <1 if < 1 = 8y – 6 and < 2 = 7y.

4. Find y.

5. If < 2 = 8x = 6 and <6 = 4x + 28, find x and < 6.

6. In the figure, m4 = 121. Find m5.

7. What is the measure of ABC?

8. If m1 = 16x - 8, m2 = 4(y + 8), and m3 = 14x + 2, find x and y.