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Warm Up If you have a laptop, connect to: www.celebratemydrive.com

Warm Up If you have a laptop, connect to: www.celebratemydrive.com And vote for Kentlake to win $100,000.00 Encourage Family and Friends to vote for Kentlake too. Simplify each expression . 1. 90 – ( x + 20) 2. 180 – (3 x – 10). 70 – x. 190 – 3 x. Correcting Assignment #3.

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Warm Up If you have a laptop, connect to: www.celebratemydrive.com

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  1. Warm Up If you have a laptop, connect to: www.celebratemydrive.com And vote for Kentlake to win $100,000.00 Encourage Family and Friends to vote for Kentlake too. Simplify each expression. 1.90 –(x + 20) 2. 180 – (3x – 10) 70 –x 190 –3x

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

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

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

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

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

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

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

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

  10. Example 1: Identifying Angle Pairs What else do we know about AEB and BED? 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.

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

  12. Example 2: Identifying Angle Pairs l m 1and 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

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

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

  15. +12 +12 –4x –4x Example 4 Continued Step 1 Find x. mJKM = mMKL Def. of  bisector (4x+ 6)° = (7x – 12)° Substitute the given values. Add 12 to both sides. 4x + 18 = 7x Simplify. Subtract 4x from both sides. 18 = 3x Divide both sides by 3. 6 = x Simplify.

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

  17. Assignment #4 pg 38-39 Foundation: 7 – 21 Core: 26, 28, 29, 33-36 Challenge: 40

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