Warm Up If you have a laptop, connect to: And vote for Kentlake to win $100, Encourage Family and Friends to vote for Kentlake too. Simplify each expression – (x + 20) – (3x – 10) 70 – x 190 – 3x

Correcting Assignment #3 Evens only in this section (6-22 even)

Correcting Assignment #3 Evens only in this section (6-22 even)

Correcting Assignment #3 Selected Problems in this section (22, 24-27, 29, 30)

Identify special angle pairs and use their relationships and find angle measures. Target Chapter 1-5 Exploring Angle Pairs

adjacent angles linear pair vertical angles complementary angles supplementary angles angle bisector Vocabulary

Vertical angles are two nonadjacent angles formed by two intersecting lines.  1 and  3 are vertical angles, as are  2 and  4. Vertical angles are congruent. Vertical Angles

An angle bisector is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK  KJM.

Adjacent, non-adjacent, vertical? Which is it? Example 1: Identifying Angle Pairs  AEB and  BED  AEB and  BED are adjacent  AEB and  CED  AEB and  CED are non-adjacent

What else do we know about  AEB and  BED? Example 1: Identifying Angle Pairs  AEB and  BED are adjacent angles that form a linear pair because they combine to create a straight angle. Linear pairs are also supplementary because they add to 180⁰.

What can we say about  3 and  5 which are formed by the intersection of lines l and m ? Example 2: Identifying Angle Pairs l m  3 and  5 are vertical angles, meaning they have the same measurement. And what about  1 and  2?

Example 2: Identifying Angle Pairs l m  1 and  2 are adjacent angles  1 and  2 are also congruent The ray between them is called an angle bisector If m  4 = 28⁰, what is m  2? m  2 = 14⁰

Find the measure of each of the following. Example 3: Finding the Measures of Complements and Supplements A. complement of  F B. supplement of  G 90  – 59  = 31  (180 – m  G)  180 – (7x+10)  = 180  – 7x – 10 = (170 – 7x)  (90 – m  F) 

Example 4: Finding the Measure of an Angle KM bisects JKL mJKM = (4x + 6)° mMKL = (7x – 12)° Find mJKM. Begin by setting the angles equal to one another. mJKM = mMKL Therefore, 4x + 6 = 7x - 12

Example 4 Continued Step 1 Find x. mJKM = mMKL (4x + 6)° = (7x – 12)° +12 4x + 18 = 7x –4x 18 = 3x 6 = x Def. of  bisector Substitute the given values. Add 12 to both sides. Simplify. Subtract 4x from both sides. Divide both sides by 3. Simplify.

Example 4 Continued Step 2 Find mJKM. mJKM = 4x + 6 = 4(6) + 6 = 30 Substitute 6 for x. Simplify.

Assignment #4 pg Foundation: 7 – 21 Core: 26, 28, 29, Challenge: 40