angles formed when two parallel lines are cut by a transversal.ppt
- 1. ANGLES FORMED WHENTWO PARALLEL LINES ARE CUT BY A TRANSVERSAL
- 2. Transversal •Definition: A line that intersects two or more lines in a plane at different points is called a transversal. •When a transversal t intersects line n and m, eight angles of the following types are formed: Exterior angles Interior angles Consecutive interior angles Alternative exterior angles Alternative interior angles Corresponding angles t m n
- 3. Corresponding Angles Corresponding Angles: Two angles that occupy corresponding positions. 3 2 6 1 2 3 4 5 6 7 8 1 5 3 7 4 8 The corresponding angles are the ones at the same location at each intersection
- 4. Angles and Parallel Lines • If two parallel lines are cut by a transversal, then the following pairs of angles are congruent. 1. Corresponding angles 2. Alternate interior angles 3. Alternate exterior angles
- 5. Proving Lines Parallel •If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. D C B A
- 6. Alternate 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. Lesson 2-4: Angles and Parallel Lines 6 3 6, 4 5 2 7, 1 8 1 2 3 4 5 6 7 8
- 7. Example: If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles when m< 1 = 100°. Justify your answers. Lesson 2-4: Angles and Parallel Lines 7 m<2=80° m<3=100° m<4=80° m<5=100° m<6=80° m<7=100° m<8=80° m<9=100° m<10=80° m<11=100° m<12=80° m<13=100° m<14=80° m<15=100° m<16=80° t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A
- 8. Proving Lines Parallel •If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. D C B A
- 12. Valuing REFLECTION: (JournalWriting) Use the quotation below as your guide in giving an example of situation on how you are going to apply your significant learnings about properties of parallel lines in your daily life. “The road of life twists, turns and no two directions are ever the same.Yet ourlessons come from the journey, not the destination’’.