Parallel lines cut_by_a_transversalpptp
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This document defines key terms related to parallel lines cut by a transversal including parallel, transversal, angle, vertical angle, corresponding angle, alternate interior angle, and alternate exterior angle. It provides examples of parallel lines cut by a transversal and identifies pairs of angles that are supplementary, vertical, corresponding, and alternate interior. It gives examples of problems identifying angle relationships and setting up and solving equations based on those relationships. Supplementary angles add to 180 degrees, corresponding angles are equal and in the same position relative to the parallel lines, and alternate interior angles are equal and on the inside of the parallel lines on opposite sides of the transversal.
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Parallel lines cut_by_a_transversalpptp
- 1. PARALLEL LINES CUT BY A TRANSVERSAL
- 2. DEFINITIONS • PARALLEL • TRANSVERSAL • ANGLE • VERTICAL ANGLE • CORRESPONDING ANGLE • ALTERNATE INTERIOR ANGLE • ALTERNATE EXTERIOR ANGLE
- 3. DEFINITIONS • SUPPLEMENTARY ANGLE • COMPLEMENTARY ANGLE • CONGRUENT
- 4. Parallel lines cut by a transversal 12 3 4 56 7 8
- 5. Parallel lines cut by a transversal 12 3 4 56 7 8 < 1 and < 2 are called SUPLEMENTARY ANGLES They form a straight angle measuring 180 degrees.
- 6. Parallel lines cut by a transversal 12 3 4 56 7 8 Name other supplementary pairs: < 2 and < 3 < 3 and < 4 < 4 and < 1 < 5 and < 6 < 6 and < 7 < 7 and < 8 < 8 and < 5
- 7. Parallel lines cut by a transversal 12 3 4 56 7 8 < 1 and < 3 are called VERTICAL ANGLES They are congruent m<1 = m<3
- 8. Parallel lines cut by a transversal 12 3 4 56 7 8 Name other vertical pairs: < 2 and < 4 < 6 and < 8 < 5 and < 7
- 9. Parallel lines cut by a transversal 12 3 4 56 7 8 < 1 and < 5 are called CORRESPONDING ANGLES They are congruent m<1 = m<5 Corresponding angles occupy the same position on the top and bottom parallel lines.
- 10. Parallel lines cut by a transversal 12 3 4 56 7 8 Name other corresponding pairs: < 2 and < 6 < 3 and < 7 < 4 and < 8
- 11. Parallel lines cut by a transversal 12 3 4 56 7 8 < 4 and < 6 are called ALTERNATE INTERIOR ANGLES They are congruent m<4 = m<6 Alternate Interior on on the inside of the two parallel lines and on opposite sides of the transversal.
- 12. Parallel lines cut by a transversal 12 3 4 56 7 8 Name other alternate interior pairs: < 3 and < 5
- 13. Parallel lines cut by a transversal 12 3 4 56 7 8 Name other alternate exterior pairs: < 2 and < 8 < 1 and < 7
- 14. TRY IT OUT 12 3 4 56 7 8 The m < 1 is 60 degrees. What is the m<2 ? 120 degrees
- 15. TRY IT OUT 12 3 4 56 7 8 The m < 1 is 60 degrees. What is the m<5 ? 60 degrees
- 16. TRY IT OUT 12 3 4 56 7 8 The m < 1 is 60 degrees. What is the m<3 ? 60 degrees
- 17. TRY IT OUT 60120 60 120 60120 60 120
- 18. TRY IT OUT x + 102x + 20 What do you know about the angles? Write the equation. Solve for x. SUPPLEMENTARY 2x + 20 + x + 10 = 180 3x + 30 = 180 3x = 150 x = 30
- 19. TRY IT OUT 2x - 60 3x - 120 What do you know about the angles? Write the equation. Solve for x. ALTERNATE INTERIOR 3x - 120 = 2x - 60 x = 60 Subtract 2x from both sides Add 120 to both sides
- 20. WEBSITES FOR PRACTICE Ask Dr. Math: Corresponding /Alternate Angles Project Interactive: Parallel Lines cut by Transversal