1.4c: Lines and Angle Relationships-proving lines parallel

GSE’s

M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons,

M(G&M)–10–9 Solves problems off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope

Corresponding s• If 2 lines are cut by a transversal so that

corresponding s are , then the lines are .

** If 1 2, then l m.

l

m

1

2

m

n

m

n

Alt. Ext. s Converse

• If 2 lines are cut by a transversal so that alt. ext. s are , then the lines are .

** If 1 2, then l m.

l

m

1

2

Consecutive Int. s Converse

• If 2 lines are cut by a transversal so that consecutive int. s are supplementary, then the lines are .

** If 1 & 2 are supplementary, then l m.

1

2

l

m

Alt. Int. s Converse

• If 2 lines are cut by a transversal so that alt. int. s are , then the lines are .

** If 1 2, then l m.

1

2l

m

Ex: Based on the info in the diagram, is p q ? If so, give a reason.

Yes, alt. ext. s conv.

No

No

p

q

p

q

p

q

Ex: Find the value of x that makes j k .

The angles marked are consecutive

interior s.

Therefore, they are supplementary.

x + 3x = 180

4x = 180

x = 45

j k

xo 3xo

Are there any parallel lines In this bookcase?

How do you know?

Suppose that maple Street and Oak Street follow a straight line path and intersect Route 6 at angles 90º

and 85º, as shown in the map below. If the streets continue in a straight line, will their paths ever cross?

Distance between a point & line

The shortest distance between a point and

A line is its perpendicular segment

R

V

m

The distance from Point R to line m is VR.

Draw the segment that would represent the distance from the point to the line.

1.

2.

3.

4.

Name the segment whose length represents the distance between the following points and lines.

1) A to BC

2) C to AB

3) B to AC

4) N to BC

Assignment