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Download Parallel Lines have special angles when they are cut by another line
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Transcript
NAME:_______________________________________________! DATE: 02/01 ASSIGNMENT: Parallel Lines and Special Angles DIRECTIONS: Parallel Lines have special angles when they are cut by another line. We call this other line a “transversal.” See the diagram below. Transversal: A line that intersects two parallel lines. In this example, it’s line “n.” Vertical Angles: The opposite angles formed when two lines intersect. Examples are angles 1 and 4, 5 and 7, 6 and 8, and 2 and 3. Vertical angles are always congruent or equal. Corresponding Angles: Angles in the same relative location at the intersection of a ! ! ! transversal and two parallel lines. Examples are angles ! ! ! 1 and 5, 3 and 8, 2 and 6, and 4 and 7. Corresponding ! ! ! angles of parallel lines are always congruent. Alternate Interior Angles: ! ! ! ! ! ! ! ! ! ! ! ! Angles on the inside of the parallel lines but on opposite sides of the transversal. Examples are angles 4 and 5; 3 and 6. Alternate Interior angles of parallel lines are congruent. Alternate Exterior Angles: ! ! ! ! ! ! ! ! ! ! ! ! Angles on the outside of the parallel lines and on opposite sides of the transversal. Examples are angles 1 and 7; 2 and 8. Alternate Exterior angles of parallel lines are congruent. Same-side Interior Angles: ! ! ! ! ! ! ! ! ! ! ! ! Angles on the inside of the parallel lines and on the same side of the transversal. Examples are angles 3 and 5; 4 and 6. Same-side interior angles of parallel lines add to 180˚. Find the measure of each angle. Also, give 1 example of each special type of angle.! ! ! ! ! ! 1.) ∠1 = ________ 2.) ∠2 = _________ 3.) ∠3 = ________ 4.) ∠4 = _________ 5.) ∠5 = ________ ! 7.) ∠7 = ________ 6.) x = _________! ! ! ! (x + 34) 8.) Vertical Angles: ______ & _______ Corresponding Angles: _____& _____ Alternate Exterior Angles: _____ & _____ Alternate Interior Angles: _____ & _____ Same-Side Interior Angles: _____ & ____ NAME:_______________________________________________! DATE: 02/01 DIRECTIONS: We learned about the angles that result from a transversal intersecting two parallel lines. Today we learn about other angle pairs. Adjacent Angles: two angles that share a vertex and a common ray ! ! Example: ∠NMO and ∠OMP here ----> Linear Pair: a special type of adjacent angles that form a straight line (180°) ! ! ! ! ! ! ! ! Example: ∠ADB and ∠BDC are adjacent and also ! form a linear pair. Complementary Angles: two angles that sum to 90° Example: ∠E and ∠F are complementary Supplementary Angles: two angles that ! ! ! sum to 180° ! ! ! ! Example: ∠F and ∠G ! are supplementary Problems: 9.) What is the complement to the ∠M? Answer: ___________ 10.) What is the supplement to ∠M? Answer: ___________ 11.) In the diagram to the right, ∠ADB and ∠BDC form a linear pair. Solve for X. X = ___________ 135° (2x − 15) NAME:_______________________________________________! Answers: 1.) 50˚ 2.) 130˚ 3.) 50˚ 4.) 130˚ 5.) 50˚ 6.) x = 16 7.) 50˚ 8.) Tutorials 9.) 63.2° 10.) 153.2° 11.) x = 30 DATE: 02/01
