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Quadrilaterals - Trapezoids, Parallelograms, Rectangles, Squares, and Rhombuses!

in his video we're going to talk about

quadrilaterals a quadrilateral is simply

a four-sided figure and it turns out

that the interior angles of a four-sided

figure adds up to 360 so in this example

angle A plus angle B plus angle C plus

angle D adds up to 360 degrees now there

are certain types of quadrilaterals that

have specific names this particular

quadrilateral is the trapezoid in this

figure these two lines are parallel now

if you have enough softly trapezoid

these two sides are congruent so make

sure you're aware of that in addition

the angles opposite to those two sides

are congruent if it's an isosceles

trapezoid the next shape that you need

to be familiar with is the parallelogram

which looks like this in the

parallelogram these two lines are

parallel and these two lines are also

parallel in addition to being parallel

the opposite sides are congruent so

those sides are congruent and these two

sides are congruent as well so that's

the parallelogram keyword parallel

opposite sides are parallel to each

other the next figure that you need to

know is the rectangle in a rectangle all

four angles are congruent they're all

right angles 90 degrees 90 times four is

360 opposite sides are congruent these

two sides are equal to each other and

the opposite sides are parallel as well

so the rectangle is like a parallelogram

but the angles are 90 so these two sides

are parallel to each other

and the top and bottom line are parallel

to each other

so that's the rectangle the next shape

that you need to be familiar with is the

rhombus in a rhombus all four sides are

congruent to each other this might not

be drawn to scale but it's supposed to

be like that let me draw a better

picture

so all four sides are congruent and the

diagonals bisect each other

at right angles so each of these angles

are right angles the square is similar

to a rhombus and a rectangle but also

different from each like a rectangle all

four angles of a square are 90 degrees

unlike a rhombus all four sides are

congruent so in a square everything is

basically equal to each other and like a

parallelogram opposite sides are

parallel to each other so each of these

shapes are known as quadrilaterals now

let's work on some math problems so

let's say if we have this four-sided

quadrilateral let's say this is X and

this angle is 58 degrees and this one is

73 and this angle is 117 degrees go

ahead and find the value of x now if you

recall the sum of all the interior

angles of a quadrilateral or four-sided

figure adds up to 360 so that means 58 +

73 + 117 + X all four angles have to add

up to 360 if we add 58 + 73 that's 131

next if we add 131 + 117 that's 248 so

248 + X is equal to 360 to find the

value of x we need to subtract both

sides by 248 so 360 - 248 that's about

112 so that's how you could find the

missing angle in a quadrilateral as long

as you keep in mind that all four angles

have to add up to 360 it's going to be a

piece of cake

these types of problems now let's work

on another example let's call this angle

a B C and D so angle a is equal to 5x

plus 10 angle B is 10 X minus 30 angle C

is 95 degrees and angle D is 4 X go

ahead and find the measure of angle a

feel free to pause the video and work on

this example so we know that all four

angles a plus B plus C plus D has to add

up to 360 angle a is 5x Plus 10 angle B

is 10 X minus 30 angle C is 95 angle D

is 4x all of that has to add up to 360

so what we need to do is combine like

terms 5x plus 10x is 15 X 15 X plus 4 X

that's 19 X negative 30 plus 95 or 95

minus 30 that's 65 65 plus 10 is 75 so

19 X plus 75 is equal to 360 now let's

subtract both sides by 75

360 minus 75 is 285 and 285 divided by

19 will give us an x value of 15 so now

that we have the value of x we could

find any angle that we want to find so

let's go ahead and find angle a so angle

a is 5 X plus 10 and let's replace X

with 15 so it's 5 times 15 plus 10 5

times 15 is 75 75 plus 10 is 85 so

that's the final answer it's 85 degrees

that's the measure of angle a now I want

to show you one of my algebra courses

that might be useful to you if you ever

need it so go to udemy.com now in the

search box just type in algebra and it

should come up so it's the one with the

image with the black background so if

you select that option and if you decide

to go to course content you can see

what's in this particular course so the

first section basic arithmetic for those

of you who want to focus on addition

subtraction multiplication and division

and it has a video quiz at the end it's

a multiple choice video quiz you can

pause it work on the problems and see

the solutions they Club is long division

multiplying to large numbers and things

like that the next tutorials on

fractions add in subtracting fractions

multiplying dividing fractions

converting fractions into decimals and

so forth so you can also take a look at

that next solve the linear equations

which we covered and just more examples

if you need more help with that the next

topic

order of operations which is also useful

graphing linear equations

you need to know how to calculate the

slope needs to be familiar with the

slope-intercept form standard form and

just how to tell of lines are parallel

perpendicular and so forth and it's a

quiz that goes with that as well

the next topic is on inequalities and

absolute value expressions which are

also seen it to the goal out of the

course and then we have polynomials and

that's a long section and then factoring

you just know the topic you need to

master and then system of equations you

can solve it by elimination substitution

there's also word problems as well

sometimes you got to solve equations

with three variables XY and Z so that

could be helpful

next quadratic equations how to use the

quadratic formula how to graph them how

to convert between standard and vertex

form and then you have rational

expressions and radical expressions

solving radical equations simplifying it

things like that and every section has a

quiz so you can always review what

you've learned if you have a test in X

day so here we have complex and major

numbers you need to know how to simplify

those exponential functions logs I have

a lot of videos on logs and then just

this is just functions in general the

vertical lines has horizontal lines has

had itself or functions even or odd and

then conic sections graph in circles had

parabolas a lips is parabolas and things

like that there's two video quizzes

because it's actually a long section and

finally arithmetic and geometric

sequences and series so that's my

algebra course if you want to take a

look at it and let me know we think