Download Section 2.2 Angles Formed by Parallel Lines

Section 2.2
Angles Formed by Parallel Lines
Goal: Prove properties of angles formed by parallel lines and a transversal, and use these
properties to solve problems.
(I)
Transversal Line
Review of Last Day
●Corresponding Angles formed by a
transversal intersecting parallel lines
are congruent.
Identify the angles.
___________
___________
___________
___________
●Supplementary Angles two angles that add to 180°.
1 2
●Vertically Opposite Angles angles formed by the intersection of two lines
that are opposite each other.
1
2
(II)
Alternate Interior, Alternate Exterior and
Interior Angles on same side of transversal.
Transversal Line
●Alternate Interior Angles
Two non-adjacent interior angles on
opposite sides of a transversal.
Identify the angles.
___________
___________
●Alternate Exterior Angles
Two exterior angles formed between two lines and a transversal, on opposite
sides of a transversal.
Identify the angles.
___________
___________
●Same Side Interior Angles
Angles formed between two lines and a transversal that lie in the interior and the same
side of a transversal.
Identify the angles.
___________
___________
http://www.mathwarehouse.com/geometry/angle/interactive-transveral-angles.php
(III) Transitive Property
If A = B and B = C then ________________
(IV) Proving Conjectures Involving Interior Angles Formed
by Parallel Lines
Alternate Interior Angles
In the diagram ∠1 = 120⁰ and line m and n are parallel
determine the value of:
∠2 = ________
∠1 = 120°
m
∠3
n
∠3 = ________
∠2
What do you notice about
alternate interior angles?
____________________________
Make a conjecture about all alternate interior angles formed by a transversal that
intersect parallel lines.
_________________________________________________________________
_________________________________________________________________
Prove the conjecture based on the diagram given below.
Line m∥ n
Statement
Justification
m
∠1
∠3
n
∠2
Alternate Exterior Angles
In the diagram ∠1 = 120⁰ and line m and n are parallel
determine the value of:
∠3 = ________
∠1 = 120°
m
∠3
n
∠2 = ________
∠2
What do you notice about
alternate exterior angles?
____________________________
Make a conjecture about all alternate exterior angles formed by a transversal that
intersect parallel lines.
_________________________________________________________________
_________________________________________________________________
Prove the conjecture based on the diagram given below.
Line m∥ n
Statement
Justification
m
∠1
∠3
n
∠2
Same Side Interior Angles
In the diagram ∠1 = 120⁰ and line m and n are parallel
determine the value of:
∠2 = ________
m
∠1 = 120°
∠3
n
∠3 = ________
∠2
What do you notice about
sum of same side interior angles?
____________________________
Make a conjecture about all same side interior angles formed by a transversal that
intersect parallel lines.
_________________________________________________________________
_________________________________________________________________
Prove the conjecture based on the diagram given below.
Line m∥ n
Statement
Justification
m
∠1
∠3
∠2
n
(V)
Summary
When a Transversal intersects parallel lines,
●corresponding angles are equal
∠___ ≅ ∠___
∠___ ≅ ∠___
∠___ ≅ ∠___
∠___ ≅ ∠___
●alternate interior angles are equal
∠___ ≅ ∠___
and
∠___ ≅ ∠___
●alternate exterior angles are equal
∠___ ≅ ∠___
and
∠___ ≅ ∠___
●same side interior angles are supplementary
∠___ + ∠___ = 180⁰
∠___ + ∠___ = 180⁰
and
(VI) Reasoning to Determine Unknown Angles
Example:
Determine the measures of:
∠a = _______
b
a
c
∠b = _______
∠c = _______
∠d = _______
d
110⁰
(VII) Using Angle Properties to Prove that Lines are Parallel
Example:
Use the angle measures to
prove that braces CG, BF
and AE are parallel.
H
D
78⁰
78⁰
C
G
35⁰
78⁰
B
78⁰
A
P.78 – 79 #1, #2, #3, #4, #8
35⁰
22⁰
F
22⁰
E