Notes

esson 5-4

If iven arallel lines then, Wa s to Prove Parallel LinesIf two lines are cut by a transversal

Corresponding angles are congruent. and form congruent corresponding(Corresponding Angles Postulate) angles.

Alternate interior angles arecongruent.Alternate exterior angles arecongruent.Same-side interior angles aresupplementary.

Parallel Lines Theorem

Lesson 5-6

Corres ondin An les Postulate

If two lines are cut by a transversaland form congruent alternate interior

angles.(Alternate Interior Angles Theorem)

If two lines are cut by a transversaland form congruent alternate exterior

angles.Alternate Exterior An les Theorem

If two lines are cut by a transversaland form supplementary same-side

interior angles.Same-Side Interior An les Theorem

Uniqueness of Parallels Theorem - Through a point NOT on a line, there isexactly one line parallel to the given line.

Trianqle Sum Theorem — The sum of the interior angles of a triangle is 180degrees.

Unique Figure — only one possible figure can be constructed using the given•nformation

Unit: Angle RelationshipsStudent Handout 1

Mcme

Date

PARALLEL LINES AND TRANSVERSALS

In the picture below, Lines X and Y cre I lines, crd Line T is a transversa I

or a line that intersects them. use a protractor to measure ecch of the 8 angles that were formed.

Lire T

Line X

Line Y

eße(i0C

What do you notice about the angle measures Q List which angles have the same measure.

Side =to

• Label the inside of the parallel lines above U lnterior", and label the outside region of the parallel

lines Exterior".

Several special pairs of angles are created when parallel lines are cut by a transversal. use the

picture above and the table to help you define and describe these types of angle pairs.

ANGLE PAIR

VERTICAL

ANGLES

STRAIGHT

ANGLES

ALTERNATE

INTERIOR ANGLES

ALTERNATE

XTERIOR ANGLES

CORRESPONDING

ANGLES

Pairs of

DEFINITION EXAMPLES RELATIONSHIP

angles formed by COOT uenb{-1 lines. e Qua\

An les that form a strai ht line and add up to. (Also called

Angles the parallel lines and onopposite sides of the

<E+C

Angles the parallel lines and onopposite sides of the

<ß+ZC7

Angles in the same relative position; angles in

-U-rx-s-——"@Maneuvering the Middle LLC, 20 '6

Back to Leggon 5-4

Name

J 5,4A Lesson Master

VOCABULARY1. In the figure at the right, identify

a. two pairs of alternate interior angles.

b. two pairs of alternate exterior angles.

c. two pairs of same-side interior angles.

d. four pairs of corresponding angles.

< If C 3

Objective B

Answer Page

Questions on SPUR ObjectivesSee Student Edition pages 302-305 for objectives.

2

56

2. Use circles to construct an equilateral triangle with aside of length PQ.

O bjective C

Fill in the Blank In 3-6, refer to the figure at the right where a Il b. a b

3. If mZ5 = 58, then rnZ—l—— is also 58.o

4. IfmZ1 + mZ2 = 142, then mZ6 =

5. If mZ7 = 137 and mZ2 = 88, then mZ1 =

6. If mZ3 = 3x + 7 and mZ6 = 4x— 5, then x =

mZ6 =

3 7

6

4

and

Geometry 233

Back to Leg n 5-4 Answer Page

Name•.

5-4A page 2

Objective G

In 7 and 8, complete the proof by writing the argument.

7. Given AB BC and BC = CDProve AB CD

jus

c

ven

3 poop.oP

8. Given ZlProve Z3 Z4< eweo

—z 3 erhcal angles 31 2 4

erhccv\

@ < 3 go-I qTraosjWe prope«h)

Objective J

In 9—11, use "Q" and "R" Streets and New Hampshire Avenueon the map of part of Washington, D.C. 4 3

9. Which numbered angle in the figure is an alternate interior 2 1

angle to Z 1?

10. IfmZ1 = 126, find 8

6 5

a. mZ2. b. mZ3.

c. mZ8. I Q.lp_ d, mZ6.

11. Q and R Streets are one-way streets. Q Street runs east while R Streetruns west.

a. If you are going east on Q Street, turn left onto New Hampshire Avenue,then turn left again onto R Street, how many degrees have you turned?

8b. How does your answer to Part a change if you turn left onto New Hampshire Avenue, then left

onto 18th street, then left again onto R Street?

234 Geometry

Back to Lesson 5-4

Name

5-4B Lesson Master

VOCABULARY

Answer Page

Questions on SPUR ObjectivesSee Student Edition pages 302-305 for objectives.

1. Refer to the diagram at the right

a. Name the interior angles. Z 2.)

b. Name the exterior angles.

c. Name the pairs of alternate interior angles.

d. Name the pairs of alternate exterior angles.

6578

4312

z i +46

SKILLS Objective B

2. Construct an equilateral triangle with side of length QL.

Objective cIn 3 and 4, use the figure at the right in which p Il q.

3. If mZ6 = 57, find the measures of the other angles.

o

4. If mZ7 = find

a. mZ2. b. mZ5

15

2 6s

37

c. mZ6.

Geometry

p

235

Back to Lesson 5-4

Name

5-4B

In 5 and 6, use the figure at the right in which s Il t.

5. IfmZ3 = 4x4 2 and mZ8 = 3x+ 20, find

b. mZ3.

6. IfmZ6 = 50n + 5 and mZ8 = 20n, find

b. mZ6.

Objective G

In 7 and 8, complete the proof by writing the argument.

7. Given B and C on @Q; Cis the midpoint of QE

Prove BQ = EC

3 Dee

Cc

5 -frCuÄSfi-we

8. Given AGHK is equilateral; % (GH) = TM.

Prove KG JH

's equal.

Objective J

1 5

8 2

47

c.mZ8. cot)

H

9. Is the sign on the street light parallel to the ground if mZ1 = 74

and mZ2 = 76? Justify your answer.

Park Blvd.1

2

Answer Page

page 2

s

c

236 Geometry