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3-1 and 3-2: Parallel Lines and Transversals. Mr. Schaab’s Geometry Class Our Lady of Providence Jr.- Sr . High School 2014-2015. Identifying Pairs of Lines. Two lines are: Parallel if they do not intersect and are coplanar . Skew if they do not intersect and are not coplanar .

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3 1 and 3 2 parallel lines and transversals

3-1 and 3-2: Parallel Lines and Transversals

Mr. Schaab’s Geometry Class

Our Lady of Providence Jr.-Sr. High School

2014-2015

identifying pairs of lines
Identifying Pairs of Lines
  • Two lines are:
    • Parallel if they do not intersect and arecoplanar.
    • Skew if they do not intersect and are not coplanar.
    • Perpendicular if they intersect to form right angles.

(Note: ALL intersecting

lines are coplanar!)

identifying pairs of lines example
Identifying Pairs of Lines - Example

In the cube below, identify the following:

  • A pair of perpendicular lines:
    • Line PS and Line PW
  • A pair of parallel lines:
    • Line PW and Line QX
    • Line PW and Line RY
    • Line QX and Line RY
  • A pair of skew lines:
    • Line PS and Line QX
    • Line PS and Line RY
identifying pairs of planes example
Identifying Pairs of Planes - Example

In the cube below, identify the following:

  • A pair of perpendicular planes:
    • Plane SRY and Plane PWZ
    • Plane PQX and Plane QXY
  • A pair of Parallel planes:
    • Plane PQX and Plane SRY
    • Plane PWZ and Plane QRY
    • Plane PQR and WXY
  • Pair of skew planes:
    • None!
angles and transversals
Angles and Transversals
  • Transversal – a line that intersects two or more coplanarlines at different points.

In the diagram on the right, line tis a the transversal of lines L1andL2.

A transversal that intersects two lines forms 8 angles, all of which have special relationships.

angle relationships
Angle Relationships
  • Corresponding Angles
    • Two angles that are in matching locations on different intersections.
    • ∠1 and ∠5 are corresponding angles.

1

5

angle relationships1
Angle Relationships
  • Alternate Interior Angles
    • Two angles that lie between the two lines and on opposite sides of the transversal.
    • ∠4 and ∠5 are alternate interior angles.

4

5

angle relationships2
Angle Relationships
  • Alternate Exterior Angles
    • Two angles that lie outside the two lines and on opposite sides of the transversal.
    • ∠2 and ∠7 are alternate interior angles.

2

7

angle relationships3
Angle Relationships
  • Consecutive Interior Angles
    • Two angles that lie between the two lines and on the same side of the transversal. These are also called “Same-side interior angles.”
    • ∠3 and ∠5 are consecutive interior angles.

3

5

angles and transversals example
Angles and Transversals - Example

Identify all pairs of angles of the given type:

  • Corresponding:
    • ∠1 & ∠5, ∠2 & ∠6, ∠3 & ∠7, ∠4 & ∠8
  • Alternate Interior:
    • ∠2 & ∠7, ∠4 & ∠5
  • Alternate Exterior:
    • ∠3 & ∠6, ∠1 & ∠8
  • Consecutive Interior:
    • ∠4 & ∠7, ∠2 & ∠5

6

5

8

7

2

1

4

3

parallel lines and transversals
Parallel Lines and Transversals
  • Corresponding Angles Postulate:
    • If two parallel lines are cut by a transversal, then all pairs of corresponding angles are congruent.
    • ∠1 ≅ ∠5

1

5

parallel lines and transversals1
Parallel Lines and Transversals
  • Alternate Interior Angles Theorem:
    • If two parallel lines are cut by a transversal, then all pairs of alternate interior angles are congruent.
    • ∠4 ≅ ∠5

4

5

parallel lines and transversals2
Parallel Lines and Transversals
  • Alternate Exterior Angles Theorem:
    • If two parallel lines are cut by a transversal, then all pairs of alternate exterior angles are congruent.
    • ∠1 ≅ ∠8

1

8

parallel lines and transversals3
Parallel Lines and Transversals
  • Consecutive Interior Angles Theorem:
    • If two parallel lines are cut by a transversal, then all pairs of consecutive interior angles are supplementary.
    • m∠3 + m∠5 = 180°

3

5

parallel lines and transversals4
Parallel Lines and Transversals
  • If you’re angle 3, then you have a lot of relationships! The other angles must really like you.
  • ∠3& ∠1 – Linear Pair (supplementary)
  • ∠3& ∠2 – Vertical Angles (congruent)
  • ∠3& ∠4 – Linear Pair (supplementary)
  • ∠3& ∠5 – Consecutive Interior Angles (supplementary)
  • ∠3& ∠6 – Alternate Interior Angles (congruent)
  • ∠3& ∠7 – Corresponding Angles (congruent)
  • ∠3& ∠8 – No relationship (∠8 is a jerk.)

1

2

3

4

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