(Complementary angles, sum = 90º) Have Out: Homework, red pen, pencil, highlighter, ruler, packet U3D2 Bellwork: If mYXZ = 64º, find mWXY. Justify and show work. mWXY + mYXZ = 180º (Linear Pair) 1. W X Y Z +1 mWXY + 64º = 180º +1 -64 -64 mWXY = 116º +1 If mABC = x, and mCBD = 2x + 6, find x. Justify and show work. 2. A B C D mABC + mCBD = 90º (Complementary angles, sum = 90º) x + 2x + 6 = 90 +1 +1 3x + 6 = 90 -6 -6 3x = 84 3 3 +1 x = 28º

Definitions: Add to your notes. Parallel lines: lines that are in the same plane and do not intersect (cross). Transversal: a line that intersects two or more lines in the same plane.

Definitions: Interior exterior exterior Add to your notes. When we classify angle relationships, we need to look at the POSITION of the angles in relation to the parallel lines AND the transversal. Interior Interior means the angles are between the parallel lines. exterior Exterior means the angles are outside the parallel lines. exterior

Definitions: Add to your notes. Two angles can be on the same side of the transversal or they can be on alternate sides of the transversal. Same side Alternate sides

Now, we put these two ideas together to classify angle relationships. Angle 4 & 5 are on alternate sides of the transversal, and are interior of the parallel lines. So, we say that angle 4 & angle 5 are Alternate Interior Angles. 2 1 4 4 3 6 5 5 8 7 **Note when we are classifying angles on parallel lines, we are dealing with PAIRS of angles classified by their positions in relation to two things: the parallel lines AND the transversal. We do NOT say that 8 is an exterior angle (this will be defined later as a single classification).

Alternate Interior Angles The angle relationships when parallel lines are cut by a transversal are… Alternate Interior Angles alternate sides of the transversal and interior of the parallels Same Side Interior Angles Same side of the transversal and interior of the parallels Alternate Exterior Angles alternate sides of the transversal and exterior of the parallels Same Side Exterior Angles Same side of the transversal and exterior of the parallels

There is one other important type of angle relationship on parallel lines cut by a transversal but it doesn’t quite follow the same ideas as the first four… Corresponding Angles Angles on the same side of the transversal and in the same position on the parallel lines (either the angles are both above or both below the parallel lines.) Since the five types of angles describe angle relationships, we can only classify PAIRS of angles as Alternate Interior Angles, Same Side Interior Angles, Alternate Exterior Angles, Same Side Exterior Angles, or Corresponding Angles. Pairs of angles can be classified as one of these relationships even if the lines being cut by the transversal are NOT parallel.

Copy the diagram and do this problem in your Notebook! Find pairs of angles that are: Same side interior angles 2 2 2 (3 & 5) or (4 & 6) 1 1 1 4 4 4 3 3 3 6 6 6 5 5 5 8 8 8 Alternate interior angles 7 7 7 (3 & 6) or (4 & 5) Alternate exterior angles Corresponding angles: (1 & 8) or (2 & 7) (1 & 5) or (2 & 6) or (3 & 7) or (4 & 8) Same side exterior angles (2 & 8) or (1 & 7)

Some pairs are equal and some are supplementary. If (and only if) the lines cut by the transversal are PARALLEL, then we can make some conclusions based on the angle relationships. Some pairs are equal and some are supplementary. b a c d f e g h

So, if the lines are parallel, what can you conclude about: Alternate Interior Angles Equal Same Side Interior Angles Supplementary Alternate Exterior Angles Equal Supplementary Same Side Exterior Angles Corresponding Angles Equal

PS-49 Complete the resource page. Use the previous definitions to classify each pair of angles. Are the angles supplementary or equal? a) Linear pair; supplementary b) Corresponding s; equal a a b b c) Alternate interior s; equal d) Same side exterior s; supplementary b a b a

f) e) a a b b g) h) a a b b i) b a PS-49 f) Corresponding s; NO conclusion (lines not //) e) Alternate exterior s; equal a a b b g) NO RELATIONSHIP h) Alternate interior s; NO conclusion (lines not //) a a b b i) Same side interior s; supplementary b a

The notes took care of problems 45 – 50! Assignment: PS 51 - 57