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Angles and Parallel Lines
When parallel lines get crossed by another line a line called a
transversal, several special angles are formed. These angles can be
made into pairs of angles which have special names.
When lines are parallel alternate interior and corresponding
angles are CONGRUENT.
Below, lines l and m are parallel and cut by the transversal t.
Two Special Angle Pairs
Two Special Angle Pairs
Name
Congruent Angles
Description
Alternate Interior Angles
4  5 and 3  6
On the opposite sides of the
transversal and on the inside
of the given lines.
Two Special Angle Pairs
Name
Congruent Angles
Description
Alternate Interior Angles
4  5 and 3  6
On the opposite sides of the
transversal and on the inside
of the given lines.
Corresponding Angles
1  5 and 2  6
4  8 and 3  7
On the same side of the
transversal and on the same
side of the given lines
Example Proof:
If two parallel lines are cut by a transversal, the
alternate interior angles are congruent.
Given m is parallel to l, prove: ∠3 = ∠6
Statement
Reason
Lines l and m are parallel
Given
Example Proof:
If two parallel lines are cut by a transversal, the
corresponding angles are congruent.
Given m is parallel to l, prove: ∠3 = ∠6
Statement
Reason
Lines l and m are parallel
Given
∠3= ∠7
Corresponding Angles
Theorem
Example Proof:
If two parallel lines are cut by a transversal, the
corresponding angles are congruent.
Given m is parallel to l, prove: ∠3 = ∠6
Statement
Reason
Lines l and m are parallel
Given
∠3= ∠7
Corresponding Angles
Theorem
∠6= ∠7
Vertical Angles
Example Proof:
If two parallel lines are cut by a transversal, the
corresponding angles are congruent.
Given m is parallel to l, prove: ∠3 = ∠6
Statement
Reason
Lines l and m are parallel
Given
∠3= ∠7
Corresponding Angles
Theorem
∠6= ∠7
Vertical Angles
∠3= ∠6
Transitive Property
Solve for x:
Solve for x:
-10 + 8x = 7x
- 10 = -x
10 = x
Check our Answer:
-10 + 8(10) = 70 degrees and 7(10) =70 deg
The angles are Corresponding so their angle
measures should be equal.
Solve for x:
Solve for x:
12x + 1 = 11x + 9
x+1 =9
x =8
Check our Answer:
12(8) + 1 = 97 degrees and 11(8) + 9 = 97 deg
The angles are alternate interior so their angle
measures should be equal.