CHAPTER 2TEST

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 twocongruent segments.

To bisect a segment means to divide the segment into two congruent segments.

Examples:

● A

● B

●M

M is midpoint of AB.

Segment Bisectors:

Examples:

1. Find AM and MB

●M

● B

● A

38

2. Find MH and GH

● H

● G

●M

18

3. Find x.

● J

●M

● K5x- 9 16

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

●D

●B

●A BD bisects ABC

ABD DBC

Examples:

1. G●

● K

●H

● J

64°

HK bisects GHJ. Find the m GHK and m KHJ.

2.

● K●J

●G

●H

145°

3.

G●

●K

H● ●

J4. ● K

●H

●G

● J

Find x.

7.H ●

J ●

K ●G ●

2x + 11

53°8.

H ● ● J

K ●

G ●

6x4x + 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°

1 2 43

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

Determine whether the angles are complementary, supplementary or neither.

1.

22°68°

2.

48°

132°

3.

41°

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 areformed by two intersecting lines.

12

34

1 and 3 are vertical angles

2 and 4 are vertical angles

Examples:

1. Find m 1

2. Find m 2

3. Find m 368°

12

3

4. Find x.

5. Find m 1

6. Find m 22x + 67 4x + 63

1

2

Two adjacent angles are a linear pair if their noncommon sides are on the same line.

5 6

common side

noncommonside

noncommonside

5 and 6 are a linear pair

EXAMPLES:

1. Find x. x 81°

2. Find y.y 136°

3. Find x.4. Find m ABD

D ●

●C

●B

●A

2x + 33 53°

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:

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 $50.

2. You need to take the ACT test your junior year of high school.

Example:

If the perimeter of a square is 24 ft, thenthe 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 statementfor the following pair of statements.

PROPERTIES OF EQUALITY AND CONGRUENCE:

PROPERTIES OF EQUALITY AND CONGRUENCE

Reflexive Property

Equality AB = AB Congruence AB ABm A = m A A A

Symmetric PropertyEquality CongruenceIf AB = CD then CD = AB If AB CD then CD ABIf m A = m B then m B = m A If A B then B A

Transitive property

Equality CongruenceIf 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

Use properties of equality:

Addition Property:

Adding the same number to each side of an equation produces an equivalent equation.

x – 3 = 7x - 3 + 3 = 7 + 3

Subtraction Property:

Subtracting the same number from each side of an equation produces an equivalent equation.

y + 5 = 11y + 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 = 72x + 4 = 2(7) + 4

8x = 16

=

x = 6x ● 4 = 6 ● 4

HomeworkPages 95-97

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