Angles Formed by Parallel Lines Cut by a Transversal
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This document discusses parallel lines and angles formed when lines are cut by a transversal. It begins by defining parallel lines and explaining that a transversal is a line that intersects two or more lines at different points. It then defines and provides examples of several types of angles formed, including alternate interior/exterior angles, same side interior/exterior angles, and corresponding angles. Groups are then assigned to prove properties of these angles for parallel lines cut by a transversal. The document concludes with practice problems finding missing angle measures using the properties and an assignment involving parallel lines cut by a transversal.
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Angles Formed by Parallel Lines Cut by a Transversal
- 2. MECHANICS The group that will win in a toss coin will have the right to choose one representative from the other group to be the opponent of their chosen representative. Then, I will ask a question. The first one who can write the answer on the board earns a point. She/ he will have the right to choose the next opponent of their next representative and so on.
- 3. Two lines are _________ if and only if they are coplanar and do not intersect.
- 4. ___________ are two angles whose measures have a sum of 180°.
- 5. ___________ are two nonadjacent angles formed by two intersecting lines.
- 6. A line that intersects two or more lines at different points is called _______.
- 7. These are pair of nonadjacent exterior angles that are on opposite sides of a transversal.
- 8. This property of real numbers states that if a+b, b+c, then a+c.
- 10. 𝐴𝐵 II 𝐶𝐷 Two lines are parallel if and only if they are coplanar and do not intersect. 𝐸𝐹 intersects 𝐴𝐵 and 𝐶𝐷 𝐸𝐹 Transversal is a line that intersects two or more lines at different points 1 2 3 4 5 6 7 8
- 11. Transversal is a line that intersects two or more lines at different points Parallel lines transversal Non-Parallel lines transversal
- 13. ALTERNATE INTERIOR/EXTERIOR ANGLES Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. 3 & 6, 4 & 5 2 & 7, 1 & 8 1 2 3 4 5 6 7 8 Interior Exterior Exterior
- 14. SAME SIDE INTERIOR/EXTERIOR ANGLES 1 2 3 4 5 6 7 8 Interior Exterior Exterior Same side angles lies on the same side of the transversal. Same Side Interior Angles: 3 and 5, 4 and 6 Same Side Exterior Angles: 1 and 7, 2 and 8
- 15. CORRESPONDING ANGLES Corresponding Angles: Two angles that occupy corresponding positions. 2 6, 1 5, 3 7, 4 8 1 2 3 4 5 6 7 8
- 17. Group 1 Group 3 Prove: 𝟑 ≅ 𝟔 Prove: 𝟑 ≅ 𝟓 are supplementary Group2 Group 4 Prove: 𝟐 ≅ 𝟕 Prove: 𝟏 ≅ 𝟕 are supplementary
- 18. If two parallel lines are cut by a transversal, then alternate interior angles are congruent. If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. If two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are supplementary. If two parallel lines are cut by a transversal, then the exterior angles on the same side of the transversal are supplementary.
- 19. Name the pairs of the following angles formed by a transversal. Line M BA Line N D E P Q G F Line L Line M BA Line N D E P Q G F Line L Line M BA Line N D E P Q G F Line L 500 1300
- 20. LET’S PRACTICE m<1=120° Find all the remaining angle measures. 1 4 2 65 7 8 3 60° 60° 60° 60° 120° 120° 120° 120°
- 21. EVALUATION Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements. 40° 120° 120° 60° 60° 40° 60° 60° 180-(40+60)= 80° 80° 80° 80° 100° 100°
- 22. ASSIGNMENT In the accompanying figure, 𝐵𝐴 II 𝐶𝐷 and 𝐷𝐸 II 𝐵𝐶. Find the value of x and 3x.