MNL appears to be what type of angle? Ya Git it? Session 2 Name all the angles having point N as their vertex. Don’t name the same angle twice. MNL appears to be what type of angle?  MNP appears to be what type of angle? The m A is 100. Solve for x. MNP, MNL, LNP L P N M acute obtuse 30 3x +10 A

Parallel Lines, Transversals, & the Angles they Create

Parallel Lines – Two lines are parallel if and only if they are in the same plane and do not intersect. B A AB CD D C

Are these grey lines parallel?

How can we connect these parallel lines? Transversal line

Constructing Parallel Lines: Math open reference Do this four times, and then label & define the special angles created: Corresponding, alternate interior, alternate exterior, consecutive interior

The angles in this figure can be compared using the following rules: Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Name the pairs of angles congruent by the Corresponding Angles Postulate.  1.  2.  3.  4.   Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the two pairs of alternate interior angles are congruent. Name the pairs of angles congruent by the Alternate Interior Angles Theorem.  5.   6. Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then the two pairs of alternate exterior angles are congruent. Name the pairs of angles congruent by the Alternate Exterior Angles Theorem.  7.   8.   Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then the two pairs of same-side interior angles are supplementary. Name the pairs of angles supplementary by the Same-Side Interior Angles Theorem.  9. 10.   Important angle relationships to note: Vertical Angles Vertical Angles are the angles opposite each other when two lines cross. They are always equal. Name the pairs of angles congruent by the definition of vertical angles.  1.  2.  3.  4.   Linear Pair A linear pair is two angles that are adjacent and supplementary Name the pairs of angles supplementary by the definition of linear pair  1.  2.  3.  4.  

Big Ideas: The Corresponding Angles Postulate states that if two parallel lines are cut by a transversal, then the pairs of corresponding angles are ____________________. 2.Congruent angles have _____________________ measures. 3. If two _________________ lines are cut by a ________________, then the two pairs of alternate interior angles are congruent. 4. If two parallel lines are cut by a transversal, then the two pairs of same-side interior angles are _____________________. 5. If two parallel lines are cut by a transversal, then the two pairs of alternate exterior angles are _____________________.

mÐABC mÐDEF

Give two examples of each kind of angle pair in the figure. Alternate interior angles Consecutive interior angles Alternate exterior angles

Tell whether lines m and n must be parallel from the given information Tell whether lines m and n must be parallel from the given information. If they are, state your reasoning. 1. Ð7 @ Ð3 2. Ð7 @ Ð6 3. Ð5 @ Ð7 4. Ð1 @ Ð5

Tell whether lines m and n must be parallel from the given information Tell whether lines m and n must be parallel from the given information. If they are, state your reasoning. 5. mÐ3 = (15x + 22)°, mÐ1 = (19x - 10)°, x = 8 6. mÐ2 = (5x + 3)°, mÐ3 = (8x - 5)°, x = 14 7. mÐ8 = (6x - 1)°, mÐ4 = (5x + 3)°, x = 9 8. mÐ6 = (x + 10)°, mÐ2 = (x + 15)°

Session 2: pg. 82 pg. 93