sat math 5 notes
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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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FEELING SQUARE? TRY ANGLES
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". & /2)/3*4
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Multiple-Choice
?A
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FEELING SQUARE? TRY ANGLES
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". & /2)/3*4
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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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FEELING SQUARE? TRY ANGLES
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!
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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
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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
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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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& O =; P ?Q;
& P ??;
=;
.
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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In this situation, if you get one angle,you can figure out 7 other angles!
Helpful Angles
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!
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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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:6 Q;
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Helpful Angles
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R P ?Q; S Q; S :6 P A6
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INSIDE A TRIANGLE
The angles add up to 180
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IR AR
RR O IR O AR P ?Q;
:R P ?Q;
R P A;
Helpful Angles
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INSIDE A TRIANGLE
The angles add up to 180
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Multiple-Choice
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FEELING SQUARE? TRY ANGLES
Multiple-Choice
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(x + 40) + (x + 50) + (2x 10) = 360
4x + 80 = 3604x = 280
x = 70
Smallest angle = x + 40 = 110
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#1&0 2- 01* V&3C* ". 01* -%&33*-0 &',3*4
The angles around a singlepoint add up to 360.
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FEELING SQUARE? TRY ANGLES
Multiple-Choice
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FEELING SQUARE? TRY ANGLES
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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FEELING SQUARE? TRY ANGLES
Multiple-Choice
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x
60
60
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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2- 6;&'+ 01* %*&-C)* ". '&$2- Q;W #1&0 2- 01* %*&-C)* ". !%&4
1. Draw a diagram
2. Given info3. All other info
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FEELING SQUARE? TRY ANGLES
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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FEELING SQUARE? TRY ANGLES
Multiple-Choice
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FEELING SQUARE? TRY ANGLES
Multiple-Choice
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2. Given info3. All other info
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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FEELING SQUARE? TRY ANGLES
Multiple-Choice
T' 01* .2,C)* &U"V*W 32'* -*,%*'0- $( &'+ &) 2'0*)-*/0 &0 X"2'0 %W &'+ $& 2-X&)&33*3 0" ()J T.* P =; &'+ + P A;W #1&0 2- 01* V&3C* ". ,4
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1. Draw a diagram
2. Given info3. All other info
ALWAYS
REMEMBER Two parallel lines being cut by a diagonal line are oftenhidden somewhere in the diagram!
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(
%
80
80
L"0*M N2,C)* '"0 +)' 0" -/&3*J
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Popular Shapes
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FEELING SQUARE? TRY ANGLES
Popular Shapes
60
60
60
x
ISOSCELES TRIANGLES
If two sides are the same, their opposite angles are the same
(and vice versa!).
x
EQUILATERAL TRIANGLES
All the sides are the same, and all the angles are 60.
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FEELING SQUARE? TRY ANGLES
Popular Shapes
a2 + b2 = c2PYTHAGOREAN THEOREM:
U
&
/
RIGHT TRIANGLES: Love them. They give so much information!
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FEELING SQUARE? TRY ANGLES
Popular Shapes
1
U
AREA FORMULA: Area = b h12
RIGHT TRIANGLES: Love them. They give so much information!
P l Sh
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FEELING SQUARE? TRY ANGLES
Popular Shapes
Area = lw
#
3
#
3
AREA FORMULA:
RECTANGLES: They have four right angles! Use that!
M lti l Ch i
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FEELING SQUARE? TRY ANGLES
Multiple-Choice
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FEELING SQUARE? TRY ANGLES
Multiple-Choice
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68
8
Q ?;
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82 + x2 = 102
x2 = 100 64
x2 = 36
x = 6
E1&0 2- 01* X*)2%*0*) ". 01* 0)&X*Z"2+ &U"V*4
M lti l Ch i
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FEELING SQUARE? TRY ANGLES
Multiple-Choice
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8 8 + 8 + 8 + 6 + 10 = 40
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FEELING SQUARE? TRY ANGLES
Multiple-Choice$
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FEELING SQUARE? TRY ANGLES
T' !$& &U"V*W !& 2- ". -. E1&0 2- 01* &)*& ". !$& 2' 0*)%- ". -4Q
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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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FEELING SQUARE? TRY ANGLES
Multiple-Choice
11
$
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h = 11Area = b h
12
Area = 81112
Area = 44
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8
Multiple Choice
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FEELING SQUARE? TRY ANGLES
Multiple-Choice
11
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5
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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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FEELING SQUARE? TRY ANGLES
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-"32+ -1"#' &U"V* #201 3*',01*W #2+01 5*W &'+ 1*2,10 !*4
Multiple-Choice
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Multiple Choice
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FEELING SQUARE? TRY ANGLES
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-"32+ -1"#' &U"V* #201 3*',01*W #2+01 5*W &'+ 1*2,10 !*4
Multiple-Choice
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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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FEELING SQUARE? TRY ANGLES
E12/1 ". 01* ."33"#2', 1&- 01* -&%* V"3C%* &- 01* )*/0&',C3&)
-"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
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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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FEELING SQUARE? TRY ANGLES
Multiple-Choice/01
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0" 01* &)*& ". 01* /2)/3*4
7B9 A
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Multiple Choice
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FEELING SQUARE? TRY ANGLES
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
x 3I78979
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7B9 A
A
Multiple Choice
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FEELING SQUARE? TRY ANGLES
Multiple-Choice/01
2
&
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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0" 01* &)*& ". 01* /2)/3*4
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Multiple-Choice
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FEELING SQUARE? TRY ANGLES
Multiple-Choice/01
2
&
1. Draw a diagram
2. Given info
3. All other info Area of circle = 12
T' 01* .2,C)* &U"V*W 12/ 2- *[C23&0*)&3 #201 -2+* 3*',01 ". QJ T. 8> 2- &
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2 3
Area of circle = r2
Area of circle = (2 3)2
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Recap
Recap
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FEELING SQUARE? TRY ANGLES
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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FEELING SQUARE? TRY ANGLES
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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FEELING SQUARE? TRY ANGLES
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
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