Download - CHAPTER 2 TEST REVIEW
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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