Challenging similarity problem | Similarity | Geometry | Khan Academy
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- เผยแพร่เมื่อ 17 ก.ย. 2024
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Interesting similarity problem where we don't have a lot of information to work with
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HARD.. I couldn't think about y-x/y = 1-x/y .
(y - x)/y = y/y - x/y so there for y/y will be 1 so we can wright it as 1 - x/y
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A simpler method is to consider the cases of parallel lines.this leads you to finding similar triangles and then by basic proportionality theorem we can easily solve.i solved it in 3 min with use of this method.ab and de are parallel by sum of cointerior angles rule. So u will find that ABC and dec are similar. Using this we can find ac:CE and then find ae and then by basic proportionality theorem we can find CF .
How did u find ac:ce
i distinctly remember this problem being given to me in 8th grade. i think i can figure it out agian :O
If it would be a mcq then we would just have to remember a formula in these questions i.e. 1/AB + 1/DE = 1/CF (atq) we just have to practice more and learn some formulas to solve problems faster
This was tough, but fun! Did it 3 times to make sure I really understand it. I would never have passed this test in high school lol
This is cool :)
it's been 9 years .... how are you, i wonder how your journey been. have a beautiful life ahead :)
can we solve it if we use 9/CF=y/y-x?????
Sir there is a question "if the areas of two similar triangles are equal prove that they are congruent ." please help me. my teacher are just avoiding me and not answering me plz help me.
Since Areas of 2 Similar Triangles are Equal,
We know that :
area(ABC)÷area(PQR) = Square of their Corresponding Sides.
Thus, Squares of all sides are equal.
Thus, All sides are equal.
Thus, By SSS ,
Triangle(ABC)≅Triangle(PQR)
What a silly questions
Common logic
awesome
HMMM. Isn't also possible to say the linesAB, CF, DE are parrallel and then find CF by doing AB times DE divided by AB plus DE on this particular problem?
Good to hear. I will hold you to it if it sux friend! Joking! Stop in some time!
A great book called "starship troopers" by Heinlein is such a great book I've actually read it 3x. The stupid, stupid movies match the book only in name. The right sfx and director i.e. Ridley Scott.
Wow !!!
Why is FE y-x? That line is longer than x. How did you determine that?
He did not
For explanation, say the y-x is z.
*VIA PROOF:*
y is the length of x and z combined (AKA x+z=y)
Subtract x from both sides to get z=y-x.
*VIA LOGIC:*
z is the length of y but without the x
z=y… minus x
*VIA EXAMPLE:*
x=3, z=5, y=z+x therefore y=8
8-3=5, every variable lines up to y-x=z
X=6, z=7, y=z+x therefore y=13
13-6=7, every variable lines up to y-x=z
Directly use the formula.. (9*12)/(9+12)
complicated much???
You just lengthened it up its just a three step sum.
How is it a 3 step sum?
@@sanchitvarshney8405we know the triangles are similar given the congruent right angles and shared angles. And since AB = 9 and DE = 12 are given, we can just skip straight to CF/9 + CF/12 = 1, and algebraically solve for CF.
But it was fun and instructive working it through step by step.
@@MichaelHollomon but if we skipped the 1st couple steps, how would we know that CF/9 + CF/12 is equal to 1? Where did 1 come from?
@@alcamisticrblx1079 1 just comes from the fact that 1 times CF equals CF. But 1 is actually an irrelevant value. You could just as easily replace it with X. In which case you would end up with CF = 36X/7, instead of the simpler CF = 36/7
Sir i have question please help me to solve this
Did you solve it yet
Anyone 2024?
Your assumption that "AB and DE are parallel" is not true because there's no indication that they actually are! that was never mentioned in the problem.
Sam Rockwell angles ABE and DEB are 90 deg each which add up to 180 . therefore the 2 lines are parrallel
Two lines are parallel if their corresponding cointerior angles sum up to 180 .this is the case here