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4.5/5.2 Parallel LinesI can prove lines parallel
I can recognize planes and transversals
I can identify the pairs of angles that are congruent given parallel lines cut by a transversal
Day 2
Find x, y, and z.
Find the perimeter of PBRE
What is a plane?►Defn: A plane is a flat surface that
continues infinitely in all directions.x
yA plane has no height, only a length and a width.
4.5/5.2 Parallel Lines
Types of lines
► There are two types of lines associated with planes.
1. Coplanar – lines, segments, or rays that lie in the same plane
2. Noncoplanar – lines, segments, or rays that do not lie in the same plane
► Lines that are coplanar can either be intersecting or parallel
►Identify the transversal in the following diagram
a
b
c
► Defn: A transversal is a line that intersects two coplanar lines.
The regions of intersecting lines
► The region between two lines is called the interior
► Everything else is the exterior
14
21a
b
interior
exterior
exterior
Parallel Lines
►Parallel line are two coplanar lines that never intersect.
►The two lines MUST be coplanar.
Alternate interior angles
► Alternate interior angles are two angles in the interior of a figure on opposite sides of the transversal.
1
2
a
b
c
If Alt. int. ∠s ≅ ⇒ ∥ lines
Alternate exterior angles
►Alternate exterior angles are angles that lie in the exterior of a figure on the opposite sides of the transversal.
If Alt. ext. ∠s ≅ ⇒ ∥ lines
1
8
c
a
b
Corresponding angles►Corresponding angles are angles on
the same side of the transversal where one angle is in the interior and one in the exterior.
5
7
If Corr. ∠s ≅ ⇒ ∥ lines
Let’s see what you know
► Based on the following diagram, name all pairs of…
1. Alternate interior angles
2. Alternate exterior angles
3. Corresponding angles
4. Vertical angles
1
2
34
56
78
a
b
c
6 ways to prove lines parallel
2. Alt. ext. ∠s≅⇒∥
4. Same side int. ∠s supp.⇒∥
5. Same side ext. ∠s supp.⇒∥
6. 2 lines ⊥ to same line⇒∥
3. Corr. ∠s≅⇒∥
1. Alt. int. ∠s ≅ ⇒ ∥ lines 1
2
34
56
78
a
b
c
►Which angle is alt. int. with ∠3?►Which angle is alt. ext. with ∠1?►Which angle is corresponding with ∠4?►Which angle is same side int. with ∠5?►Which angle is same side ext. with
∠1?
A little review
8 765
4 321