3-1 Properties of Parallel Lines L.E.Q. What special angles are created by two lines cut by a transversal and how are they related?
Remember: What would you call two lines which do not intersect? Parallel A solid arrow placed on two lines of a diagram indicate the lines are parallel. The symbol || is used to indicate parallel lines. AB || CD
What is a transversal? A transversal is a line which intersects two or more lines in a plane. The intersected lines do not have to be parallel. Lines j, k, and m are intersected by line t. Therefore, line t is a transversal of lines j, k, and m.
Pairs of Angles Formed By 2 Lines Cut By a Transversal
Alternate interior angles Two nonadjacent interior angles on opp. Sides of the transversal 3 and 6 4 and 5
Same side interior angles Two interior angles on the same side of the transversal 4 and 6 3 and 5
Corresponding angles 2 and 6 1 and 5 3 and 7 4 and 8 Two angles in corresponding position relative to the two lines 2 and 6 1 and 5 3 and 7 4 and 8
Which angle is the same side interior angle to D? A E F H C A B D C F E G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Which angle is the alternate interior angle to D? A E F H C A B D C F E G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Which angle is the corresponding angle to C? A E F H G A B D C F E G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Identifying Corresponding Angles List all the sets of corresponding angles: 1&5, 2&6, 3&7, 4&8 t 1 2 3 4 5 6 7 8
Identifying Alternate Interior Angles List all the sets of alternate interior angles: 3&6, 4&5 t 1 2 3 4 5 6 7 8
Identifying Same-Side Interior Angles List all the sets of same-side interior angles: 3&5, 4&6 t 1 2 3 4 5 6 7 8
Corresponding Angles Postulate If 2 parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 2
Alternate Interior Angles Theorem If 2 parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 3 4
Same-Side Interior Angles Theorem If 2 parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary. 5 6
If angle 1 is 47 degrees find the following: Can you determine the measure of specific angles with given information? If angle 1 is 47 degrees find the following: Angle 4 Angle 5 Angle 2 Angle 8
EXAMPLE: Using algebra to find angle measures. Find the values of x and y. Then find the measures of the angles. 2x y y - 50
Hw: pg 118-119 #s 1-16 skip 9