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Properties of Parallel Lines: Postulates and Theorems, Study notes of Analytical Geometry and Calculus

University of Louisiana at Lafayette (UL)Analytical Geometry and Calculus

The notes from a geometry class on the properties of parallel lines, including Postulates 3-1 (Same-Side Interior Angles) and theorems 3-1 (Alternate Interior Angles), 3-2 (Corresponding Angles), and 3-3 (Alternate Exterior Angles). Examples and homework problems are also included.

What you will learn

  • What is the Corresponding Angles Theorem and how is it used to find congruent angles?
  • What is Postulate 3-1 in geometry?
  • How do alternate interior angles relate to parallel lines?

Typology: Study notes

2021/2022

Uploaded on 09/27/2022

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11/5/2012
1
Section 3-2
Properties of
Parallel Lines –
Day 1,
Calculations.
Michael Schuetz
Postulate 3-1: Same-Side
Interior Angles Postulate.
Postulate
If l//m
Then
If a transversal
intersects two
parallel lines,
then same-
side interior
angles are
supplementary
l
m
12
43
56
87
10485mm
10386mm
pf3
pf4
pf5

Partial preview of the text

Download Properties of Parallel Lines: Postulates and Theorems and more Study notes Analytical Geometry and Calculus in PDF only on Docsity!

Section 3-

Properties of

Parallel Lines –

Day 1,

Calculations.

Michael Schuetz

Postulate 3-1: Same-Side

Interior Angles Postulate.

Postulate

If

l//m

Then

If a transversal

intersects two

parallel lines,

then same-

side interior

angles are

supplementary

l

m

m  4  m  5  1 0 8

m  3  m  6  1 0 8

Theorem 3-1: Alternate Interior

Angles Theorem. (AIA)

Theorem

If

l//m

Then

If a transversal

intersects two

parallel lines,

then alternate

interior angles

are congruent.

l

m

Theorem 3-2: Corresponding

Angles Theorem. (Corr )

Theorem

If

l//m

Then

If a transversal

intersects two

parallel lines,

then

corresponding

angles are

congruent.

l

m

 ' s

Example 2, Angle Measure

 What is the value of y? Which theorem or

postulate justifies your answer?

l p q

 40  80 180 o o o o

 y  

Same-Side

Interior Postulate

tells us that

y˚

 40  100 o o o

 y 

o o

y 

Homework: Day 1

 P. 153, #’s 7-9, 12-20, 22, 27-

Section 3- Properties of Parallel Lines – Day 2, Proofs. Michael Schuetz Proof of Theorem 3-1: AIA  Given: l//m  Prove: ^4  ^6 l m

Statements Reasons

  1. l / / m 1. Given
    1. m  3  m  4  180 o 2. Supplementary Angles
    2. m  3  m  6  180 o 3. Same-Side Interior Angles Postulate
    3. m  3  m  4  m  3  m  (^6) 4. Transitive Property of Equality
  2. m  4  m  (^6) 5. Subtraction Property of Equality
    1.  4   6 6. Definition of Congruence