targets identify relationships between two lines or two planes. name angle pairs formed by parallel...

• Identify relationships between two lines or two planes.

• Name angle pairs formed by parallel lines and transversals

Lesson 3-1: Parallel Lines & Transversals

TARGETS

Lines & Planes

LESSON 3-1: Parallel Lines & Transversals

Two lines intersect in a point

Two planes intersect in a line

A line intersects a plane at a point

Model the following situations in the items on your desk

Parallel and Skew


Parallel lines -

Skew lines -

Parallel planes -

Coplanar lines that DO NOT intersect

Planes that DO NOT intersect

Lines that DO NOT intersect and are not coplanar

QuickTime™ and a decompressor

are needed to see this picture.

€

JK LM

QuickTime™ and a decompressor

are needed to see this picture.

€

Plane B Plane A

Lines l and m are skew lines

Lines & Planes


3) Two lines are skew

2) Two planes are parallel

Model the following situations in the items on your desk

1) Two lines are parallel.

4) Two lines are parallel. Both lines intersect a plane in 2 distinct points.

5) Two lines intersect a plane in two distinct points. The two lines are skew.

Identify Parallel and Skew Relationships

AD, EH, FG

A. Name all segments parallel to BC.


EXAMPLE 1

B. Name a segment skew to EH.

AB, CD, BG, or CF

C. Name a plane parallel to plane ABG.plane CDE

A. Name a plane that is parallel to plane RST.


EXAMPLE 1 Identify Parallel and Skew Relationships

B. Name a segment that intersects YZ.

C. Name a segment that is parallel to RX.

plane WXY

WZ, XY, TS, or SY

QW, TZ, or SY

Transversal

A line that intersects two ormore coplanar lines at two different points

1

42

3

8 7

65

q

d

r


line d

Interior Angles

Lie in the region between linesq and r

1

42

3

8 7

65

q

d

r


<3, <4, <5, <6

Exterior Angles

Lie in the two regions notbetween lines q and r

1

42

3

8 7

65

q

d

r


<1, <2, <3, <4

Consecutive Interior Angles

A pair of interior angles that lie on the same side of

the transversal (d )

1

42

3

8 7

65

q

d

r


<4 & <5

<3 & <6

Alternate Interior Angles

Nonadjacent interior angles that lie on opposite sides of


1

42

3

8 7

65

q

d

r


<3 & <5

<4 & <6

Alternate Exterior Angles

Nonadjacent exterior angles that lie on opposite sides of


1

42

3

8 7

65

q

d

r


<1 & <7

<2 & <8

Corresponding Angles

Lie on the same side of transversal ( d ) and on the same side of lines q and r

1

42

3

8 7

65

q

d

r


<1 & <5 ; <2 & <6<3 & <7 ; <4 & 8

Classify Angle Pair Relationships

Classify the relationship between the following angle pairs alternate interior, alternate exterior, corresponding, or consecutive interior angles.

corresponding


EXAMPLE 2

A. 2 and 6

B. 1 and 7alternate exterior

C. 3 and 8consecutive interior

D. 3 and 5alternate interior

A. 4 and 5.


EXAMPLE 2 Classify Angle Pair Relationships

consecutive interior

B. 7 and 9.corresponding

C. 4 and 7.alternate exterior

D. 2 and 11.alternate interior

Classify the following relationships:

Identify Transversals and Classify Angle Pairs

BUS STATION The driveways at a bus station are shown. Identify the transversal connecting the angles and then classify the relationship between the pair of angles.


EXAMPLE 3

A. 1 and 2

B. 2 and 3

C. 4 and 5

line v; corresponding angles

line v; alternate interior angles

line y; consecutive interior angles

HIKING A group of nature trails is shown. Identify the sets of lines to which the given line is a transversal:


EXAMPLE 3 Identify Transversals and Classify Angle Pairs

A. line a lines c, d, e, f

B. line b

C. line c

lines c, d, e, f

lines a, b, d, e, f

targets identify relationships between two lines or two planes. name angle pairs formed by parallel...

Documents

parallel skew parallel

plane parallel

lines q

parallel model

id parallel skew relationships

skew lesson

transversals lesson

segment skew