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Angle Measures and Parallel Lines

Learn about the relationship between angle measures when parallel lines are cut by a transversal. This resource provides examples, vocabulary, and practice exercises to help understand the concept.

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Angle Measures and Parallel Lines

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  1. Lines Section 5.1 Essential question: How are the measures of angles related when parallel lines are cut by a transversal? https://www.brainpop.com/math/geometryandmeasurement/parallelandperpendicularlines/

  2. Vocabulary When two lines intersect in a plane and form right angles they are called __________________________. Two lines are called _________________ when they are in the same plane and do not intersect.

  3. Graphic Organizer

  4. Key Concept: Transversals and Angles • A line that intersects two or more lines is called a _______________, and eight angles are formed • ______________ lie inside the lines. • Examples: ___________________ • ______________ lie outside the lines. • Examples: ___________________

  5. Key Concept: Transversals and Angles • __________________ are interior angles that lie on opposite sides of the transversal. When the lines are parallel, their measures are equal. Examples: ________________ • __________________ are exterior angles that • lie on opposite sides of the transversal. When the • lines are parallel, their measures are equal. • Examples: ____________________

  6. Key Concept: Transversals and Angles • ___________________ are those angles that are in • the same position on the two lines in • relation to the transversal. When the lines • are parallel, their measures are equal. • Examples: ______________________

  7. Examples • Classify each pair of angles in the figure as alternate interior, alternate exterior, or corresponding. • 1. ∠4 and ∠8 • 2. ∠1 and ∠7 • 3. ∠2 and ∠6

  8. Notes: Find Missing Angle Measures • When two parallel lines are cut by a transversal, special angle relationships exist. • If you know the measure of one of the angles, you can find the measures of all of the angles. • Suppose you know that the measure of angle 1 is equal to 50 degrees. You can use that to find the measures of angles 2, 3, and 4. m∠ 2 = Because ______________________________ m ∠ 3 = Because ______________________________ m ∠ 4 = Because _______________________________

  9. Examples If m∠4 = 122°, find each given angle measure. Justify your answer. 1. m∠8 2. m∠5 3. m∠2 4. m∠1

  10. Essential Question • How are the measures of the angles related when parallel lines are cut by a transversal? • ______________________________________________________________________________ • ______________________________________________________________________________ • ______________________________________________________________________________ • ______________________________________________________________________________

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