Parallel Lines & Transversals 8th Math Presented by Mr. Laws Geometry Parallel Lines & Transversals 8th Math Presented by Mr. Laws t m n

Standard 8.G.5 – Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Essential Question Can you describe what happens to two parallel lines once they are cut by a transversal?

Parallel Lines & Transversals Parallel Line are two lines that are next to each other on the same plane. They will never cross or intersect each other. Example: Line M is parallel to Line N (M II N) T M N Transversals is a line that crosses or intersects parallel lines, which form specific angles. Example: Line T is a transversal.

Interior Angles T M N 1 2 3 4 5 6 7 8 Interior Interior Angles are angles that lie on the inside of the two parallel lines. The form supplementary angles which will equal to 1800. Examples: 3 and 4 5 and 6

Exterior Angles T M N 1 2 3 4 5 6 7 8 Exterior Exterior Exterior Angles are angles that lie on the outside of the two parallel lines. The form supplementary angles which will equal to 1800. Examples: 1 and 2 7 and 8

Alternate Interior Angles M N 1 2 3 4 5 6 7 8 Alternate Interior Angles are angles that lie on the inside of the two parallel lines and on the opposite side of the transversal. They are congruent (same) to each other. Examples: 3 6 4 5 ≅

Alternate Exterior Angles M N 1 2 3 4 5 6 7 8 Alternate Exterior Angles are angles that lie on the outside of the two parallel lines and on the opposite side of the transversal. They are congruent (same) to each other if the lines are parallel. Examples: 1 8 2 7 ≅

Vertical Angles T M N 1 2 3 4 5 6 7 8 Vertical angles are angles that lie across from each other on the opposite side of the transversal. If the two lines are parallel, they are congruent to each other. Example: 1 4 2 3 ≅ 5 8 6 7 ≅

Corresponding Angles ≅ ≅ T M N 1 2 3 4 5 6 7 8 Corresponding Angles are angles that lie on the same side of the transversal and on the same side of the parallel line. They are congruent if the lines are parallel. Example: 1 5 2 6 ≅ 4 8 3 7 ≅

Adjacent Angles T M N 1 2 3 4 5 6 7 8 Adjacent Angles are angles that lie next to each other. They form supplementary angles that are equal to 180 degrees.: 3 and 4 5 6 7 8 1 2 2 and 4 5 7 6 8 1 3

Angle Relationships Angle Relationships - a straight line is measure 180 degrees. When cut by a transversal or line perpendicularly, the total measure of the angles must equal to an 180 degrees. For Example: 1800 1500 300

What are the Missing Angles ? 2 = 3 4 1 350 T M N 1 2 3 4 6 = 7 8 5 5 6 7 8

Answers 2 = 3 4 1 350 T M N 1450 1450 1 2 350 3 4 6 = 7 8 5 350 5 6 1450 7 8 1450 350

Summary Can you answer the essential question? Is there any more questions concerning this lesson? What are some key concepts to remember about this lesson?