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. To bisect a segment means to divide the segment into two congruent segments. Examples: ● ● ● A M B M is midpoint of AB. Examples: 1. Find AM and MB 38 ● ● ● A M B 2. Find MH and GH ● ● ● G M H 18 3. Find x. ● J 5x- 9 ● M 16 ● K HOW TO FIND MIDPOINT: 1. (7,-8) and (9,2) 2. (-14,7) and (-4,-15) 3. (-6,-10) and (-4,-3) ANGLE BISECTORS: An angle bisector is a ray that divides an angle into two angles that are congruent. ● A ● D BD bisects ABD ● B ● C ABC DBC Examples: HK bisects 1. GHJ. Find the m G ● GHK and m KHJ. 2. ●K ● J ● K 64° ● J 145° ● H ● H ● G 3. H ● ● J ● K G● 4. ●K ● J ● H ● G Find x. H● 7. 2x + 11 J ● 8. G● 53° G● K ● K● 6x H● 4x + 8 What is the m What is the m ● J GHK and m GHJ. KHJ. 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° 1 2 Angles 1 and 2 are supplementary. 3 4 Angles 3 and 4 are complementary. Determine whether the angles are complementary, supplementary or neither. 1. 2. 68° 132° 22° 48° 41° 3. 48° 4. 145° 42° 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. VERTICAL ANGLES: Two angles are vertical angles if they are not adjacent and their sides are formed by two intersecting lines. 2 1 4 3 1 and 3 are vertical angles 2 and 4 are vertical angles Examples: 1. Find m 1 2. Find m 2 3. Find m 3 2 1 3 68° 4. Find x. 5. Find m 1 6. Find m 2 2x + 67 1 2 4x + 63 Two adjacent angles are a linear pair if their noncommon sides are on the same line. common side 5 noncommon side 5 and 6 noncommon side 6 are a linear pair EXAMPLES: 1. Find x. x 81° y 136° 2. Find y. 3. Find x. 4. Find m D● ABD ● A 2x + 33 ● B 53° ● C 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 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. 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. 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. PROPERTIES OF EQUALITY AND CONGRUENCE: PROPERTIES OF EQUALITY AND CONGRUENCE Reflexive Property Equality AB = AB m A=m Congruence A Symmetric Property Equality If AB = CD then CD = AB If m A = m B then m B = m A AB ≅ AB A≅ A Congruence If AB ≅ CD then CD ≅ AB If A ≅ B then B ≅ A Transitive property Equality If AB = CD and CD = EF, then AB = EF. Congruence If AB ≅ CD and CD ≅ EF, then AB ≅ EF. If m A = m B and m B = m C, then m A = m C. If A ≅ B and then A ≅ C B≅ C, 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 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 8𝑥 16 = 8 8 Substitution Property: Substituting a number for a variable in an equation produces an equivalent equation. x=7 2x + 4 = 2(7) + 4 Homework Pages 95-97 {1-26}