Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Riemannian connection on a surface wikipedia , lookup

Duality (projective geometry) wikipedia , lookup

Rational trigonometry wikipedia , lookup

Contour line wikipedia , lookup

Perspective (graphical) wikipedia , lookup

Euclidean geometry wikipedia , lookup

Line (geometry) wikipedia , lookup

Transcript
```Advanced Geometry
Parallel and Perpendicular Lines
Lesson 3
Proving Lines Parallel
Reasons
Before we can prove that lines are parallel we need
to add to our list of reasons.
Corresponding Angles Postulate
If two lines in a plane are cut by a transversal so that
corresponding angles are congruent, then the lines are
parallel.
There are several theorems that can be proven
using the Corresponding Angles Postulate.
If two lines in a plane are cut by a transversal so that a
pair of alternate exterior angles is congruent, then the two
lines are parallel.
To prove lines are parallel, you must use one
of the following postulates or theorems:
If corresponding angles are ,
then the lines are parallel.
If AEA are ,
then the lines are parallel.
If AIA are ,
then the lines are parallel.
If CIA are supplementary,
then the lines are parallel.
You may also
have to use the
converse of a
postulate or
theorem to
justify a
statement.
Given: 1   2
Prove:
AB || CD
Use the original
theorem.
If AIA are ,
the lines are ||.
Given:
AB || CD
Prove: 1   2
Use the converse.
If the lines are ||,
AIA are .
More Theorems
If a line is perpendicular to one of two parallel lines,
then it is perpendicular to the other.
If two lines are perpendicular to the same line,
then the lines are parallel.
Given: m  n and m  p
Prove: n p
Given: 1  2 and 1  3
Prove: LM QN
Given: CA DB
1  3
2  4
Prove: DA EB
Given: PLM  MNP
NPL and PLM are
supplementary.
Prove: LP MN
Given: WZ  ZY and 1  2
Prove: WX  WZ
```
Related documents