Pgs 26 28 30 Warmup pg 23 The measures of 2 Vertical Angles are 90 and 5x 10 Find the value of x The measure of an angle is twice the measure of its compliment Whats a Transversal ID: 730498
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Slide1
4.2 Transversals and Parallel Lines
Pgs. 26, 28, 30Slide2
Warmup
(pg. 23)
The measures of 2 Vertical Angles are 90 and (5x + 10). Find the value of x.
The measure of an angle is twice the measure of its compliment. Slide3
What’s a Transversal?
A
transversal
is a line that intersects two coplanar lines at two different points.
transversal
p
q
1 2
4 3
5 6
8 7Slide4
Angle Pairs Formed by the Transversal
Corresponding
Angles
Same side of trans
& intersecting lines
Exs
:
∠1 & ∠5 ∠4 & ∠8
∠2 &
∠6 ∠3 & ∠7
Same Side Interior Angles (SSI)
Same side of the trans, and inside the linesExs:
∠4 & ∠5 ∠3 & ∠6Same Side Exterior Angles (SSE)
Same side of the trans, and
outside
the lines
Exs: ∠1 & ∠8∠2 & ∠7Alternate Interior Angles (AIA)Opposite non-adjacent angles on the inside of linesExs: ∠3 & ∠5∠4 & ∠6Alternate Exterior Angles (AEA)Opposite non-adjacent angles on the outside of linesExs: ∠1 & ∠7∠2 & ∠8Slide5
Parallel Lines
2 lines that never meet
When parallel lines are cut by a transversal, the angle pairs formed are either
congruent
or
supplementary
. Slide6
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 -30
m∠5 = 150
m∠5 = 150°
*Postulate can be applied to Same Side Exterior Angles tooSlide7
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 tooSlide8
Proof:
1. Given
2. Same Side Interior Angles
3. From pic/ given
4.
Def
of Supp.
5. Def. of LP
6. Transitive
P.o.E.
7. Subtraction
P.o.E.
1.
p
//
q
2. ∠3 & ∠6 are supp.
3. ∠5 & ∠6 are LP4. m∠3 + m∠6 = 1805. m∠5 + m∠6 = 180 6. m∠3 + m∠6 = m∠5 + m∠6 7. m∠3 = m∠5 Slide9
Corresponding Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Slide10
Proof:
1. Given
2. From pic/given
3. AIA Postulate
4. From pic/given
5. VA
Thm
6. Substitution
P.o.E.
1.
p
//
q
2. ∠4 & ∠6 are AIA
3. m∠4 = m∠6
4.
∠6
& ∠8 are VA5. m∠6 = m∠8 6. m∠4 = m∠8Slide11
ExamplesSlide12
ExamplesSlide13
ExamplesSlide14
Examples