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Aim:. k. 1. 2. 3. 4. 6. How do we prove lines are parallel?. 5. l. 7. 8. Do Now:. 1) Name 4 pairs of corresponding angles. 2) Name 2 pairs of alternate interior angles. 3) Name 2 pairs of alternate exterior angles.

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Aim

Aim:

k

1

2

3

4

6

How do we prove lines are parallel?

5

l

7

8

Do Now:

1) Name 4 pairs of corresponding angles.

2) Name 2 pairs of alternate interior angles.

3) Name 2 pairs of alternate exterior angles.

4) If lines l and k are extended and they never intersect, what can we say about l and k ?

l || k

5) If lines l and k are extended and they do intersect, what can we say about l and k ?

l is not || k

Geometry Lesson:


Def parallel

Def: Parallel lines have no points in common or have all points in common.

B

F

D

A

E

C

l

k

Line m is “transverse” to lines l and k.

m

Def. Parallel:

Def: Transversal

Def: A transversal is a line that intersects two other lines in two different points.

Geometry Lesson: Proving Lines are Parallel


Transversals angle pairs

4

8

3

7

2

6

1

5

Transversals/ angle pairs:

Geometry Lesson: Proving Lines are Parallel


Ex transversals angle pairs

7

5

4

6

3

2

1

1

2

3

4

Ex: Transversals/ angle pairs

State the type of each angle pair:

alt. interior

corresponding

alt. interior

alt. exterior

alt. interior

alt. interior

Geometry Lesson: Proving Lines are Parallel


Proving lines parallel

l

4

8

Theorem #11:

3

7

2

Two lines cut by a transversal are parallel if a pair of corresponding angles are congruent.

6

1

5

Theorem #12:

Two lines cut by a transversal are parallel if a pair of alternate interior angles are congruent.

Theorem #13:

Two lines cut by a transversal are parallel if a pair of interior angles on the same side of the transversal are supplementary.

Theorem #14:

Two lines perpendicular to the same line are parallel.

Proving lines parallel

m

k

Geometry Lesson: Proving Lines are Parallel


Ex proving lines parallel

1)

E

(

D

C

(

A

B

A

B

C

D

2)

3)

E

4)

48

D

132

C

(

C

D

)

A

B

A

B

Ex: Proving lines parallel

Or

Geometry Lesson: Proving Lines are Parallel


Ex proving lines parallel1

D

C

A

B

?

Ex: Proving lines parallel

Geometry Lesson: Proving Lines are Parallel


Ex proving lines parallel2

C

Given:

1

3

D

B

2

Prove:

A

Ex Proving lines parallel:

Given

Given

Def. angle bisector

Transitive Postulate

Geometry Lesson: Proving Lines are Parallel


Proving lines parallel1

R

L

D

A

S

S

Q

M

3) Given:

E

F

Prove:

P

D

1

2

3

4

M

B

R

C

Proving lines parallel:

1) Given:

Prove:

2) Given:

Prove:

Geometry Lesson: Proving Lines are Parallel


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