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3-1, 3-2 Parallel Lines & Transversals.ppt

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The document discusses different types of angles formed when lines are intersected by a transversal line, including corresponding angles, alternate interior angles, same side interior angles, vertical angles, and linear pairs. It provides examples of naming angles based on their relationship and shows that corresponding angles are congruent, alternate interior angles are congruent, and same side interior angles are supplementary, even when the lines are not parallel. Examples are worked through to demonstrate finding unknown angle measures.

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Jim Smith JCHS Section 3-1, 3-2
A Line That Intersects 2 Or More Lines At Different Points Is Called A Transversal transversal
When This Happens, 8 Angles Are Formed
This Forms 2 Neighborhoods
Remember Vertical And Linear Angles Vertical
Linear Pairs
These Angles Are Called Consecutive Or Same Side Angles
Interior Angles (Between 2 lines) Exterior Angles (outside the lines)
Alternate Angles Are On Different Sides Of The Transversal And From Different Neighborhoods Alternate Exterior Angles 1 And 8 Angles 2 And 7 Alternate Interior Angles 3 And 6 Angles 4 And 5
Consecutive Int Angles 3 and 5 Angles 4 and 6 Consecutive Ext Angles 1 and 7 Angles 2 and 8
Corresponding Angles Are Located In The Same Position In Each Neighborhood
11 12 13 14 15 16 17 18 Name The Angles 1. 11 and 15 2. 12 and 16 3. 13 and 16 4. 12 and 18 5. 14 and 16 6. 14 and 18 7. 11 and 14 8. 15 and 17
1.Corresponding 2.Corresponding 3.Alt Interior 4.Consecutive (SS) Exterior 5.Consecutive (SS) Interior 6.Corresponding 7.Vertical 8.Linear
1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 With This Diagram, We Can Work With Angles In Different Neighborhoods As Long As They Are Connected By A Transversal Name the angles 1. 1 and 3 2. 7 and 12 3. 11 and 14 4. 6 and 10 5. 13 and 5 6. 9 and 6 7. 1 and 13 8. 5 and 4 9. 7 and 11 10. 6 and 11
1. Corresponding 2. Alt. Int. 3. Alt. Int. 4. Cons. (SS) Int. 5. Corresponding 6. Alt. Int. 7. Consecutive Ext 8. Alt. Ext 9. Cons. (SS) Int. 10.None
3-1, 3-2 Parallel Lines & Transversals.ppt
3-1, 3-2 Parallel Lines & Transversals.ppt
a b
If 2 Parallel Lines Are Cut By A Transversal Then: Corresponding Angles Are Congruent Alternate Interior Angles Are Congruent Same Side Interior Angles Are Supplementary
Remember ……… Even Without Parallel Lines Vertical Angles Are Always Congruent Linear Pairs Are Always Supplementary
1 2 3 4 5 6 7 8 a b a b m 1 = 105 Find: 1. 3 = 2. 6 = 3. 7 = 4. 4 = 5. 5 = 75 75 75 105 105
1 2 3 4 5 6 7 8 a b 63° 117° 119° 119° 119° 119° 61° 63° 63°
a b 2x+6 3x-10 5x-20 2x-10 2x+6 = 3x-10 6 = x – 10 16 = x 5x-20+2x-10 = 180 7x-30 = 180 7x = 210 x = 30 4x+25 6x-15 4x+25 = 6x-15 25 = 2x-15 40 = 2x 20 = x

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3-1, 3-2 Parallel Lines & Transversals.ppt