Math 7 geometry 04 angles, parallel lines, and transversals - grade 7
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The document discusses angles and parallel lines. It defines parallel lines and transversals, and explains that when a transversal intersects parallel lines, it forms eight angles that can be classified as vertical, corresponding, alternate interior, alternate exterior, adjacent, consecutive interior, and consecutive exterior angles. The document states that if two parallel lines are cut by a transversal, vertical angles, corresponding angles, alternate interior angles, and alternate exterior angles are congruent, while adjacent angles, consecutive interior angles, and consecutive exterior angles are supplementary. An example problem demonstrates finding angle measures given one is known.
Math 7 geometry 04 angles, parallel lines, and transversals - grade 7
- 2. A Mathematics 7 Lecture Next Century Mathematics: The New Grade 7 Angles and Parallel Lines
- 3. Parallel Lines: A Review Definition: Two lines are parallel if they lie on the same plane but do not intersect. m n Line m is parallel to line n Symbol: m || n Angles and Parallel Lines
- 4. Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal. t m n Line t is a transversal Angles and Parallel Lines
- 5. Transversal When a transversal t intersects line n and m, eight angles of the following types are formed: Exterior angles Interior angles Vertical Angles Linear Pairs Alternative exterior angles Alternative interior angles Corresponding angles t m n Angles and Parallel Lines
- 6. Angles and Parallel Lines t m n We’ll consider the angles formed by a pair of parallel lines cut by a transversal and their properties. When a transversal t intersects parallel line n and m, eight angles of the following types are formed: Vertical Angles Linear Pairs Corresponding angles Alternate exterior angles Alternate interior angles Consecutive interior angles Consecutive exterior angles Angles and Parallel Lines
- 7. If two parallel lines are cut by a transversal, then the following pairs of angles are congruent: 1. Vertical Angles 2. Corresponding angles 3. Alternate interior angles 4. Alternate exterior angles Angles and Parallel Lines t m n Angles and Parallel Lines
- 8. Vertical Angles Vertical Angles: 1 4, 2 3, 5 8, 6 7 Two angles that are opposite angles. Vertical angles are congruent. 1 2 3 4 5 6 7 8 Vertical angles are congruent Angles and Parallel Lines
- 9. 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 Corresponding angles are congruent Angles and Parallel Lines
- 10. Alternate Angles Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal but are not a linear pair 3 6, 4 5 1 2 3 4 5 6 7 8 Alternate interior angles are congruent Angles and Parallel Lines
- 11. Alternate Exterior Angles Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. 2 7, 1 8 1 2 3 4 5 6 7 8 Alternate exterior angles are congruent Angles and Parallel Lines
- 12. If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary: 1. Adjacent angles 2. Consecutive interior angles 3. Consecutive exterior angles Angles and Parallel Lines t m n Angles and Parallel Lines
- 13. Adjacent Angles 1 & 2 , 2 & 4 , 4 &3, 3 & 1, 5 & 6, 6 & 8, 8 & 7, 7 & 5 Adjacent angles form linear pairs; i.e., they form a 180 angle 1 2 3 4 5 6 7 8 Adjacent angles are supplementary Angles and Parallel Lines
- 14. Consecutive Angles Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. m3 +m5 = 180º, m4 +m6 = 180º 1 2 3 4 5 6 7 8 Angles and Parallel Lines Consecutive interior angles are supplementary
- 15. Consecutive Angles Consecutive Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. m1 +m7 = 180º, m2 +m8 = 180º 1 2 3 4 5 6 7 8 Angles and Parallel Lines Consecutive exterior angles are supplementary
- 16. Example 1: In the figure, line AB is parallel to line CD and s is a transversal. g h fe ac db s DC BA a. Give all pairs of angles falling under the following: vertical, corresponding, alternate interior, alternate exterior, adjacent Examples Angles and Parallel Lines
- 17. Example 1: Answer g h fe ac db s DC BA Examples Angles and Parallel Lines Vertical Corresponding Alternate interior Alternate exterior Adjacent
- 18. Example 1: In the figure, line AB is parallel to line CD and s is a transversal. g h fe ac db s DC BA b. If ma = 100, find the measures of all the other angles Examples Angles and Parallel Lines 100
- 19. Example 1b: If ma = 100, here are the measures of the other angles: g h fe ac db s DC BA Examples Angles and Parallel Lines 100 100 80 80 100 80 80 100
- 21. Thank you!