CHAPTER 2 TEST REVIEW

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

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

2.Find MH and GH ● H ● G ●M●M 18

3.Find x. ● J ●M●M ● K 5x- 916

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. ●C●C ●D●D ●B●B ●A●A BD bisects ABC ABD DBC

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

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

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

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° Angles 1 and 2 are supplementary.Angles 3 and 4 are complementary.

Determine whether the angles are complementary, supplementary or neither ° 68° 2. 48° 132° 3. 41° 48° ° 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 and 3 are vertical angles 2 and 4 are vertical angles

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

4.Find x. 5.Find m 1 6.Find m 2 2x x

Two adjacent angles are a linear pair if their noncommon sides are on the same line. 56 common side noncommon side noncommon side 5 and 6 are a linear pair

EXAMPLES: 1. Find x.x81° 2. Find y. y136°

3.Find x. 4.Find m ABD D ● ●C●C ●B●B ●A●A 2x °

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. HYPOTHESISCONCLUSION

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

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

Example: 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. Use the law of syllogism to write an if-then statement for the following pair of statements.

PROPERTIES OF EQUALITY AND CONGRUENCE: PROPERTIES OF EQUALITY AND CONGRUENCE

Use properties of equality: Addition Property: Adding the same number to each side of an equation produces an equivalent equation. x – 3 = 7 x = 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. Division Property: Dividing each side of an equation by the same nonzero number produces an equivalent equation. Substitution Property: Substituting a number for a variable in an equation produces an equivalent equation. x = 7 2x + 4 = 2(7) + 4 x = 6 x ● 4 = 6 ● 4

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