Download Module 4.2 Notes

4.2 Transversals and
Parallel Lines
Pgs. 26, 28, 30
Warmup (pg. 23)
1. The measures of 2 Vertical Angles are 90 and
(5x + 10). Find the value of x.
2. The measure of an angle is twice the measure of
its compliment.
What’s a Transversal?
A transversal is a line that intersects two coplanar
lines at two different points.
 transversal
1 2
4 3
5 6
8 7
p
q
Angle Pairs Formed by the Transversal
Corresponding Angles Same side of trans &
intersecting lines
Exs:
∠1 & ∠5
∠2 & ∠6
Same Side Interior
Angles (SSI)
Same side of the trans, Exs:
∠4 & ∠5
and inside the lines
∠3 & ∠6
Same Side Exterior
Angles (SSE)
Same side of the trans, Exs:
∠1 & ∠8
and outside the lines
∠2 & ∠7
Alternate Interior
Angles (AIA)
Opposite nonadjacent angles on
the inside of lines
Exs:
∠3 & ∠5
∠4 & ∠6
Alternate Exterior
Angles (AEA)
Opposite nonadjacent angles on
the outside of lines
Exs:
∠1 & ∠7
∠2 & ∠8
∠4 & ∠8
∠3 & ∠7
Parallel Lines
2 lines that never meet
When parallel lines are cut by
a transversal, the angle pairs
formed are either congruent or
supplementary.
Same Side Interior Postulate
If two parallel lines are cut by a transversal, then the pairs of same-side interior
angles are supplementary.
Ex: m∠4 = 30°. Find m∠5.
m∠5 + 30 = 180
- 30
m∠5
-30
= 150
m∠5 = 150°
*Postulate can be applied to Same Side Exterior Angles too
Alternate Interior Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of Alternate Interior
Angles are congruent.
*Postulate can be applied to Alternate Exterior Angles too
Proof:
1. p // q
1. Given
2. ∠3 & ∠6 are supp.
2. Same Side Interior Angles
3. ∠5 & ∠6 are LP
3. From pic/ given
4. m∠3 + m∠6 = 180
4. Def of Supp.
5. m∠5 + m∠6 = 180
5. Def. of LP
6. m∠3 + m∠6 = m∠5 + m∠6
6. Transitive P.o.E.
7. m∠3 = m∠5
7. Subtraction P.o.E.
Corresponding Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of corresponding
angles are congruent.
Proof:
1. p // q
1. Given
2. ∠4 & ∠6 are AIA
2. From pic/given
3. m∠4 = m∠6
3. AIA Postulate
4. ∠6 & ∠8 are VA
4. From pic/given
5. m∠6 = m∠8
5. VA Thm
6. m∠4 = m∠8
6. Substitution P.o.E.
Examples
Examples
Examples
Examples