sat math 5 notes

8/12/2019 SAT Math 5 Notes

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Feeling square? Try angles

Math 5

Geometry


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FEELING SQUARE? TRY ANGLES

Todays Lesson

Look for parallel lines, supplemental angles, etc.

Manipulate right and non-right triangles

Approach all SAT geometry questions

Today you will learn how to

Find the area and volume of various shapes


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Multiple-Choice

?A

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Multiple-Choice

1

3! 360 = 120

1

3

1

3

1

6

1

6! 360 = 60

1

6

120 60 = 60

?A

?:


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Recap


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Recap

Make sure to obey the variable rules!

Plug inANSWERS if youre trying to find the value of a variable.

Plug in NUMBERS if you see variables in the answers.

Use a Goal Number when you can!


7/49FEELING SQUARE? TRY ANGLES

Points, Lines and y = mx + b

ORIGIN the point (0, 0)

PARALLEL two slopes are the same

PERPENDICULAR two slopes multiply to 1

INTERCEPT where the line crosses an axis

SLOPE

Wicked Important Terms:

how steep a line is


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SAT Geometry

Approach



Geometry

1. Draw a diagram (if there isnt one already).

2. Fill in ALL given information.

B',3* B8< %*&-C)*- 56

D1* )*/0&',3* EFGH 1&- &' &)*& ". I5J

K*,%*'0 !" 2- 0#2/* &- 3"', &- -*,%*'0 !$J

Every SAT geometry question can be done the exact same way:

J



Geometry

1. Draw a diagram (if there isnt one already).

2. Fill in ALL given information.

3. Fill in ALL other information you can figure out.

POPULAR SHAPES

(isosceles triangles, right triangles,squares, and rectangles)

Every SAT geometry question can be done the exact same way:

HELPFUL ANGLES

(90vertical, supplementary)


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Helpful Angles



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Helpful Angles

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=;

.

ON A STRAIGHT LINE

The angles add up to 180



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&=;

Helpful Angles

VERTICAL ANGLES

The angles across from each other are equal.

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=;



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&=;

=;

=; &

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In this situation, if you get one angle,you can figure out 7 other angles!

Helpful Angles

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!

=;

PARALLEL LINES

When theyre cut by a diagonal line, all the small angles

are the same, and all the big angles are the same.

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Helpful Angles

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Q; O :6 O R P ?Q;

R P ?Q; S Q; S :6 P A6

.

INSIDE A TRIANGLE




IR AR

RR O IR O AR P ?Q;

:R P ?Q;

R P A;

Helpful Angles

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.

INSIDE A TRIANGLE




Multiple-Choice

R O 5;

IR S ?;

R O 6;

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Multiple-Choice

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R O 5;

IR S ?;

R O 6;

(x + 40) + (x + 50) + (2x 10) = 360

4x + 80 = 3604x = 280

x = 70

Smallest angle = x + 40 = 110

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The angles around a singlepoint add up to 360.


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Multiple-Choice

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Multiple-Choice

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1. Draw a diagram

2. Given info

60

60

603. All other info

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ALWAYS

REMEMBER

If all the sides of a triangle are equal, then all the

angles are 60.

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2- 6;&'+ 01* %*&-C)* ". '&$2- Q;W #1&0 2- 01* %*&-C)* ". !%&4


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Multiple-Choice

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x

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60

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ALWAYS

REMEMBER

If two sides of a triangle are the same, immediately

write down that their opposite angles are the same!

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1. Draw a diagram

2. Given info3. All other info


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Multiple-Choice

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1. Draw a diagram

2. Given info

65

65

60

60

60

8050

65 + 40 + b = 180

40

b

105 + b = 180

b = 75

3. All other info

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When the three angles ofa triangle are all in terms

of one variable, you shouldsolve for that variable!


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Multiple-Choice

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Multiple-Choice

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When two parallel lines are sliced through, all the smallangles are the same, and all the big angles are the same.

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(1. Draw a diagram

> >

80

80

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Multiple-Choice

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1. Draw a diagram


ALWAYS

REMEMBER Two parallel lines being cut by a diagonal line are oftenhidden somewhere in the diagram!

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80

80

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Popular Shapes


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Popular Shapes

60

60

60

x

ISOSCELES TRIANGLES

If two sides are the same, their opposite angles are the same

(and vice versa!).

x

EQUILATERAL TRIANGLES

All the sides are the same, and all the angles are 60.


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Popular Shapes

a2 + b2 = c2PYTHAGOREAN THEOREM:

U

&

/

RIGHT TRIANGLES: Love them. They give so much information!


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Popular Shapes

1

U

AREA FORMULA: Area = b h12

RIGHT TRIANGLES: Love them. They give so much information!

P l Sh


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Popular Shapes

Area = lw

#

3

#

3

AREA FORMULA:

RECTANGLES: They have four right angles! Use that!

M lti l Ch i


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Multiple-Choice

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Multiple-Choice

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8

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82 + x2 = 102

x2 = 100 64

x2 = 36

x = 6

E1&0 2- 01* X*)2%*0*) ". 01* 0)&X*Z"2+ &U"V*4

M lti l Ch i


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Multiple-Choice

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8 8 + 8 + 8 + 6 + 10 = 40

68

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Multiple-Choice$

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Multiple-Choice

11

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Variables in the answers and in terms of inthe prompt; plug in and use the Goal Number!

1. Draw a diagram

2. Given info

3. All other info

M ltiple Choice


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Multiple-Choice

11

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h = 11Area = b h

12

Area = 81112

Area = 44

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Multiple Choice


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Multiple-Choice

11

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44 is our Goal Number!

Plug in h= 11in the Answer Choices!

16(112)

11= 176

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Multiple Choice


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Multiple-Choice

B )*/0&',C3&) -"32+ #201 3*',01 I*W #2+01 IRW &'+ 1*2,10*7B9

B /CU* #201 *+,* !I*789B /CU* #201 *+,* ! x79

B /(32'+*) #201 )&+2C-*&'+ 1*2,10 I*7@9

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Multiple Choice


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-"32+ -1"#' &U"V* #201 3*',01*W #2+01 5*W &'+ 1*2,10 !*4

Multiple-Choice

B )*/0&',C3&) -"32+ #201 3*',01 I*W #2+01 IRW &'+ 1*2,10*7B9

B /CU* #201 *+,* !I*789B /CU* #201 *+,* ! x79

B /(32'+*) #201 )&+2C-*&'+ 1*2,10 I*7@9

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*

5*

Volume = b hw

ALWAYS

REMEMBER

This formula, along with many others, will be on the

test. That does NOT mean you shouldnt memorize it!

Multiple Choice


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-"32+ -1"#' &U"V* #201 3*',01*W #2+01 5*W &'+ 1*2,10 !*4

Multiple-Choice

B )*/0&',C3&) -"32+ #201 3*',01 I*W #2+01 IRW &'+ 1*2,10*7B9

B /CU* #201 *+,* !I*789B /CU* #201 *+,* ! x79

B /(32'+*) #201 )&+2C-*&'+ 1*2,10 I*7@9

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*

5*

Volume = b hw

Volume = (x)(4x)( x)

Volume = 4 x3

D: 4 x3

Volume of cylinder: r2h

D: ( )(2x)2(x)

Multiple Choice


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Multiple-Choice/01

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0" 01* &)*& ". 01* /2)/3*4

7B9 A

A

Multiple Choice


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Multiple-Choice/01

2

&

1. Draw a diagram

2. Given info

3. All other info

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30

Super-Popular Shape:The 30-60-90 Triangle!

x

2x

4

30

60

84 3

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A

Multiple Choice


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Multiple-Choice/01

2

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1. Draw a diagram

2. Given info

3. All other info

If BD is 4 3,

then DQ%C-0 U* 2 32 3

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Multiple-Choice


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Multiple-Choice/01

2

&

1. Draw a diagram

2. Given info

3. All other info Area of circle = 12

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+2&%*0*) ". 01* /2)/3* #201 /*'0*) &W 01*' #12/1 ". 01* ."33"#2', 2- *[C&3

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7B9 A

A

2 3

Area of circle = r2

Area of circle = (2 3)2


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Recap

Recap


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Recap

Geometry

Fill in every given piece of information.

Angles

On a straight line, angles add up to 180.

Use Helpful Angles and Popular Shapes to get more information!

Triangles

The angles in an equilateral triangle are each 60.

If two sides are the same, then the opposite angles are also the same.

In a triangle, angles add up to 180.

Around a single point, angles add up to 360.

Recap


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Recap

Make sure to obey the variable rules!

Plug inANSWERS if youre trying to find the value of a variable.

Plug in NUMBERS if you see variables in the answers.

Use a Goal Number when you can!

Recap


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Recap

If all the sides of a triangle are equal, then all the angles are 60

.

Two parallel lines being cut by a diagonal line are often hidden

somewhere in the diagram!

Volume and area formulas will be on the test, but that does NOT

mean you shouldnt memorize them!

ALWAYS REMEMBER


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SESSION MATERIALS

Whats next?

Make sure you download the Class Notes to your computer

to print out or study later! They are in each live class and

also on your homepage under Session Study Materials.

Also be sure you have the KnewtonKnotes, which are

printable study sheets for every section of the test!

Study the

sat math 5 notes

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