Parallel Lines With Transversals

These are Parallel Lines V A B V C D

Line AB || Line CD V A B V C D

This is the transversal

This transversal slices and dices 2 parallel lines.

When you slice 2 || lines, 8 special angles are formed. 1 2 V 3 4 5 6 V 7 8

Corresponding Angles Same Spot Different Line

Corresponding Congruent Remember… Corresponding Congruent

The line below is a mirror image of the line above it. 1 2 V 3 4 5 6 V 7 8

5 is the corresponding angle to 1 5 is the corresponding angle to 1. It is in the same spot on the line below. Corresponding angles are congruent. 1 2 V 3 4 5 6 V 7 8

6 is the corresponding angle to 2 6 is the corresponding angle to 2. It is in the same spot on the line below. Corresponding angles are congruent. 1 2 V 3 4 5 6 V 7 8

7 is the corresponding angle to 3 7 is the corresponding angle to 3. It is in the same spot on the line below. Corresponding angles are congruent. 1 2 V 3 4 5 6 V 7 8

? is the corresponding angle to 4? 1 2 V 3 4 5 6 V 7 8

Interior Angles Inside the Football Field

Inside the 2 Parallel Lines. Interior Angles V V Inside the 2 Parallel Lines.

Remember… Interior means Inside

Interior Angles: The 4 angles in-between the 2 parallel lines. 1 2 V 3 4 5 6 V 7 8

Same-side Interior Angles Are Hanging Out on The Same Side of The Transversal.

Same Side Supplemental Interior Angles Are Supplemental Same Side Supplemental

Same Side Supplemental Remember… Same Side Supplemental

Same-Side Interior Angles: The 2 angles on the same side of the transversal 1 2 V 3 4 5 6 V 7 8

Same-Side Interior Angles: These 2 are also on the same side of the transversal. 1 2 V 3 4 5 6 V 7 8

Same-Side Interior Angles: Are Supplemental V 3 5 V Angle 3 + Angle 5 = 180

Example: Same-Side Interior Angles: Are Supplemental V 55 ? V 55 + ? = 180

Same-Side Interior Angles: Are Supplemental V 55 125 V 55 + 125 = 180

Same-Side Interior Angles: Are Supplemental V 70 x V 70 + x = 180

Same-Side Interior Angles: Are Supplemental V 70 X = 110 V 70 + 110 = 180

Same-Side = Supplemental 120 + x = 180 V 120 x V x = 60

Alternate Interior Angles Are Congruent They are the same!

Alternate Interior Angles: Are on opposite sides of the the transversal. 1 2 V 3 4 5 6 V 7 8

Alternate Interior Angles: Are on opposite sides of the the transversal. 1 2 V 3 4 5 6 V 7 8

Alternate Interior Angles: Are congruent 1 2 V 3 4 5 6 V 7 8

Alternate Interior Angles: Are congruent V 160 x V What is x? x = 160

Why? Because they are part of the 2 sets of vertical angles that are congruent 1 2 V 3 4 5 6 V 7 8

These 2 sets of vertical angles are also congruent 1 2 V 3 4 5 6 V 7 8

Exterior Angles Outside the Football Field

External Angles are OUTSIDE the Football Field 1 2 V V 7 8

And now, time for Dramatic Kitty

A Parallel Lines with Transversals Puzzle

Find the remaining angle measures. ? ? V 50 ? ? ? V ? ?

Vertical Angles. ? 50 V 50 ? ? ? V ? ?

Corresponding Angles (One Line Below) ? 50 V 50 ? 50 ? V 50 ?

Same Vertical Angles One Line Below ? 50 V 50 ? ? 50 V 50 ?

Same Side Supplemental ? 50 V 50 130 130 50 V 50 ?

(or Alternate Exterior Angles) Vertical Angles (or Alternate Exterior Angles) 130 50 V 50 130 130 50 V 50 130

A Parallel Lines with Transversals Puzzle With Algebra

Find the value of x. 50 V X + 1 V

Corresponding Angles are Equal. 50 V X + 1 V X + 1 = 50 X = 49

Find the value of x. V 5x - 16 2X + 20 V

Alternate Interior Angles are Congruent. V 5x - 16 2X + 20 V 5X - 16 = 2X + 20 X = 12

Now try some problems on your own.