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CHAPTER 2 TEST REVIEW

CHAPTER 2 TEST REVIEW. Segment Bisectors:. The midpoint of a segment is the point on the segment that divides it into two congruent segments. A segment bisector is a segment, ray, line, or plane that intersects a segment at Its midpoint.

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CHAPTER 2 TEST REVIEW

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  1. CHAPTER 2 TEST REVIEW

  2. Segment Bisectors: The midpoint of a segment is the point on the segment that divides it into two congruent segments. A segment bisector is a segment, ray, line, or plane that intersects a segment at Its midpoint. To bisect a segment means to divide the segment into two congruent segments. Examples: ● A ● M ● B M is midpoint of AB.

  3. Examples: 1. Find AM and MB 38 ● A ● M ● B

  4. 2. Find MH and GH ● G ●M ● H 18

  5. 3. Find x. ● J ●M ● K 5x- 9 16

  6. HOW TO FIND MIDPOINT: (7,-8) and (9,2) (-14,7) and (-4,-15) (-6,-10) and (-4,-3)

  7. ANGLE BISECTORS: An angle bisector is a ray that divides an angle into two angles that are congruent. ● A ● D BD bisects ABC ABD DBC ● C ● B

  8. Examples: HK bisects GHJ. Find the m GHK and m KHJ. 1. G ● 2. ● K ● J ● K 64° 145° ● J ● H ● H ● G

  9. H ● ● J 3. 4. ● K ● K ● J ● H ● G G●

  10. Find x. J ● H ● 2x + 11 7. 8. G ● 53° K ● K ● 6x G ● 4x + 8 ● J H ● What is the m GHK and m KHJ. What is the m GHJ.

  11. COMPLEMENTARY AND SUPPLEMENTARY ANGLES: Two angles are complementary angles if the sum of their measure is 90° Two angles are supplementary angles if the sum of their measures is 180° 3 1 2 4 Angles 1 and 2 are supplementary. Angles 3 and 4 are complementary.

  12. Determine whether the angles are complementary, supplementary or neither. 1. 2. 68° 132° 22° 48° 41° 48° 3. 4. 145° 42°

  13. Measures of compliments and supplements: 1. A and B are complements. If m A = 23° find m B. 2. C and D are supplements. If m C = 113° find m D. 3. E and F are supplements. If m E = 39° find m F.

  14. VERTICAL ANGLES: Two angles are vertical angles if they are not adjacent and their sides are formed by two intersecting lines. 2 1 3 4 1 and 3 are vertical angles 2 and 4 are vertical angles

  15. Examples: Find m 1 Find m 2 Find m 3 1 2 68° 3

  16. Find x. Find m 1 Find m 2 1 4x + 63 2x + 67 2

  17. Two adjacent angles are a linear pair if their noncommon sides are on the same line. common side 5 6 noncommon side noncommon side 5 and 6 are a linear pair

  18. EXAMPLES: 1. Find x. x 81° 2. Find y. y 136°

  19. D ● Find x. Find m ABD 2x + 33 53° ● A ● B ● C

  20. IF-THEN STATEMENTS AND DEDUCTIVE REASONING: An if-then statement has two parts. The “if”part contains the hypothesis. The “then” part contains the conclusion. If a number is divisible by 2 then the number is even. HYPOTHESIS CONCLUSION

  21. EXAMPLES: Identify the hypothesis and the conclusion. 1. If it rains today then the game will be cancelled. 2. If angle is 120° then it is obtuse.

  22. Write if-then statements: 1. I will buy the cell phone if it costs less then $50. 2. You need to take the ACT test your junior year of high school.

  23. Example: Use the law of syllogism to write an if-then statement for the following pair of statements. If the perimeter of a square is 24 ft, then the length of a side of the square is 6 ft. If the length of a side of a square is 6 ft, then the area of the square is 36 square feet.

  24. PROPERTIES OF EQUALITY AND CONGRUENCE: PROPERTIES OF EQUALITY AND CONGRUENCE Reflexive Property Equality AB = AB Congruence AB AB mA = m A A A Symmetric Property Equality Congruence If AB = CD then CD = AB If AB CD then CD AB If m A = m B then m B = m A If A B then B A

  25. Transitive property Equality Congruence If AB = CD and CD = EF, If AB CD and CD EF, then AB = EF. then AB EF. If m A = m B and m B = m C, If A B and B C, then m A = m C. then A C

  26. Use properties of equality: Addition Property: Adding the same number to each side of an equation produces an equivalent equation. x – 3 = 7 x - 3 + 3 = 7 + 3 Subtraction Property: Subtracting the same number from each side of an equation produces an equivalent equation. y + 5 = 11 y + 5 – 5 = 11 – 5

  27. Multiplication Property: Multiplying each side of an equation by the same nonzero number produces an equivalent equation. x = 6 x ● 4 = 6 ● 4 Division Property: Dividing each side of an equation by the same nonzero number produces an equivalent equation. 8x = 16 = Substitution Property: Substituting a number for a variable in an equation produces an equivalent equation. x = 7 2x + 4 = 2(7) + 4

  28. Homework Pages 95-97 {1-26}

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