Triangle similarity
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Similar Triangle Basics
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Similarity Postulates
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Similar triangles 1
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Similar triangles 2
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Similar Triangle Example Problems
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Similarity Example Problems
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Solving similar triangles 1
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Similarity example where same side plays different roles
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Solving similar triangles 2
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Challenging Similarity Problem
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Finding Area Using Similarity and Congruence
Similarity example where same side plays different roles The same side not corresponding to itself in two similar triangles
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- In this problem we're asked to figure out the length of BC
- We have a bunch of triangles here in some lengths of sides
- and a couple of right angles,
- and so maybe we can establish similarity between some
- of the triangles
- There's actually 3 different triangles that I can see here,
- this triangle, this triangle and this larger triangle
- If we can establish some similarity here,
- maybe we can use ratios between sides
- somehow to figure out what BC is
- So when you look at, you have a right angle right over here,
- so, you, in triangle BDC, you have one right angle,
- in triangle ABC you another right angle
- If can we share, if we can show that they have another angle
- or another corresponding set of angles
- that are congruent to each other,
- then we can show that they're similar
- And actually both of those triangles, both BDC and ABC,
- both share this angle right over here
- So if they share that angle, then they definitely share two angles
- So they both share that angle right over there
- Let me do that in a different color just for
- just to make it different than those right angles
- They both share that angle there,
- and so we know that two triangles
- that have at least two of their angles
- are, are that at least have two congruent angles,
- they are going to be similar triangles
- so we know, we know that triangle, I'll write this,
- triangle ABC, ABC, we went from the unlabeled angle
- to the right, yellow right angle to the orange angle
- So let me write it this way
- Went from the unlabelled angle right over here
- to the orange angle or to the yellow angle
- I'm having trouble with colors
- to the orange angle, ABC
- And we want to do this very carefully here,
- because the same points or the same vertices may not say,
- play the same role in both triangles
- We want to make sure we're getting the similarity right
- White vertex to the 90 degree angle vertex to the orange vertex
- That is going to be similar to, to triangle
- So which is the one that is neither right angle?
- So we're looking at the smaller triangle right over here
- Which is the one that is, neither a right angle
- or the orange angle what's going to be vertex B
- Vertex B had the right angle
- when you think about the larger triangle but we haven't thought
- about just that little angle right over there
- So we have started vertex B then we're going to go to the right angle,
- the right angle is vertex D, vertex D,
- and then we go to vertex C which is in orange
- Show, so we have shown that they are similar
- And now that we're si that we know
- that they're similar, we can attempt to take ratios between the sides
- And so let's think about it, we know what the length
- of AC is AC is going to be, AC is going to be equal to 8, 6 plus 2
- So we know that AC, AC, what's the corresponding side
- on this triangle right over here
- So you can learn to look at the letters, A and C
- is going to corres is going to correspond to BC,
- the first and the third, first and the third
- AC is going to correspond to BC
- And what is and so this is interesting
- cause we're already involving BC
- And so, what is going to correspond to
- And then if we look at BC on the larger triangle,
- so if we look at BC on the larger triangle,
- BC is going to correspond to what on the smaller triangle?
- It's going to correspond to DC
- And it's good because we know what AC is and we know what DC is
- And so we can solve for BC
- So I want to take one more step to fi
- to show you what we just did here
- Cause BC is playing two different roles
- On this first statement right over here,
- we're thinking of BC, BC corresponds
- BC on our smaller triangle corresponds to AC on our larger triangle
- And then in our, in the second statement BC
- on our larger triangle corresponds to DC on our smaller triangle,
- so in both of these cases, so these are our larger triangles
- And then these are, this is from the smaller triangle right over here,
- corresponding sides
- And this is a cool problem because BC plays two different roles
- in two, in both triangles
- But now we have enough information to solve for BC
- We know that AC is equal to 9
- We know that A oh sorry, AC is equal to 8,
- AC is equal to 8, 6 plus 2 is 8
- And we know that DC is equal to 2, that's given
- And now we can cross multiply,
- 8 times 2 is 16 is equal to BC times BC is equal to BC squared
- And so BC is going to be equal to the principle root of 16 which is 4
- BC is equal to 4, BC is equal to 4 and we're done
- And the hardest part about this problem is just realizing that BC
- plays two different roles and just keeping your head straight is,
- and just keeping your head straight on those two different roles
- And just to make it clear,
- let me actually draw these two triangles separately
- So if I drew ABC separately it would look like this,
- it would look like this
- So this is my triangle ABC and then this is a right angle,
- this is our orange angle
- We know that the length of this side right over here is 8
- And we know that the length of this side,
- what we figured out thru this problem is 4
- Then if we want to draw BDC we would draw it like this
- So BDC BDC looks like this
- So this is BDC, that's a little bit easier
- to visualize cause we've already
- this is our right angle,
- this is our orange angle and this is four
- and this right over here is two
- And I did it this way to show you that you kinda have to flip
- this triangle over and rotate it
- just to have kind of a similar orientation
- and then it might make it look a little bit clearer
- So if you've found this part confusing,
- I encourage you to try to flip and rotate BDC
- in such a way that it seems to look a lot like ABC
- And then this ratio should hopefully make a lot more sense
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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