Congruence postulates
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Congruent Triangles and SSS
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SSS to Show a Radius is Perpendicular to a Chord that it Bisects
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Other Triangle Congruence Postulates
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Two column proof showing segments are perpendicular
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Finding Congruent Triangles
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Congruency postulates
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More on why SSA is not a postulate
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Perpendicular Radius Bisects Chord
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Congruent Triangle Proof Example
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Congruent Triangle Example 2
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Congruent triangles 1
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Congruent triangles 2
Congruent Triangles and SSS What it means for triangles to be congruent
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- So, this diagram over here, I have this big triangle
- I have all these little triangles inside of this big triangle.
- And what I wanna do is see if I could figure out the measure
- of this angle, right here.
- And we'll call that measure theta.
- And they tell us a few other things,
- you might have seen this symbol before
- these means they are right angles
- or that they have a measure of 90 degrees.
- So, that's a 90 degree angle, that is a 90 degree angle
- and that is a 90 degree angle over there.
- And they also tell us that this angle over here is 32 degrees.
- So, let's see what we can do,
- and maybe we can solve this in multiple different ways.
- That's what really fun about this,
- there's multiple ways to solve these problems.
- So, if this angle is theta, we have theta is adjacent to this angle,
- it's adjacent to this green angle.
- And if you add them together you're gonna get this right angle
- you're gonna get this right angle.
- So, this pink angle, theta, plus this green angle
- must be equal to 90 degrees.
- When you combine them, you get a right angle.
- So, you could call this one,
- it's measure is gonna be 90 minus theta.
- And now we have, now we have 3 angles in the triangle
- and we just have to solve for theta.
- Because we know that this angle plus this angle plus this angle
- are gonna be equal to 180 degrees.
- So you have 90 minus theta plus 90 degrees, so plus 90 degrees
- plus 90 degrees plus 32 degrees,
- so we're gonna use a different color,
- plus 32 degrees, plus 32 degrees is going to be equal to 180 degrees.
- The sum of the of the measures of the angle
- inside the triangle add up to 180 degrees.
- That's all we're doing over here.
- And so let's see if we can simplify this a little bit.
- So if we subtract these 2 guys, 90 plus 90 is gonna be a 180
- so you get 180 minus theta plus 32 is equal to 180 degrees.
- And then we have, what else do we have?
- We have a 180 on both sides,
- we can subtract that from both sides.
- So, that cancels out that goes to 0.
- And you have negative theta plus 32 degree is equal to 0.
- You could add theta to both sides
- and you get 32 degrees is equal to theta
- or theta is equal to 32 degrees.
- So, it's gonna be actually the same measure as this angle over here.
- That's one way to the do the problem.
- There's other ways that we could have done the problem.
- We could have said and actually there's a ton of ways
- we could have done this.
- We can look at this big triangle over here,
- we can say look if this is 90 degrees over here
- this is 32 degrees over here, this angle up here
- is gonna be 180 minus 90 degrees minus 32 degrees.
- Because they all have to add up to 180 degrees.
- And I just kinda skipped a step over there,
- obviously this, actually let me not skip a step.
- Let me call this X, if we call that the measure of that angle X
- we would have X plus 90,
- I'm looking at the biggest triangle in this diagram right here.
- X plus 90 plus 32 plus 32 is going to be equal 180 degrees.
- And so, if you subtract 90 and 32 from both sides,
- so if you subtract 90 from both sides
- you get X plus 32 is equal to 90.
- And if you subtract 32 from both sides you get X is equal to
- What is this?
- 58 degrees, X is equal to 58 degrees.
- X is equal to 58 degrees.
- Fair enough.
- What else could we figure out?
- Well if this angle here, if this angle over here is a right angle.
- And I'm just redoing the problem all over again,
- just to show you there's multiple ways to get the answer.
- We were given, if this is a right angle,
- if that is 90 degrees, then this angle over here is supplementary to it
- and it also has to be 90 degrees.
- So we have this angle plus 90 degrees plus this angle,
- plus this angle, plus this angle have to equal to 180,
- maybe we can call that Y.
- So Y plus 58 plus 90 is equal to 180.
- You can subtract 90 from both sides, subtract 90 from both sides.
- This will become 90, subtract 58 from both sides
- you get Y is equal to 32 degrees.
- Y is equal to 32 degrees.
- Well if Y is equal to 32 degrees, it's is complimentary
- it is complimentary to this angle right over here.
- it is complimentary, I'll give it a new color.
- Not supplementary, it's complimentary it adds up to 90 degrees.
- It is complimentary to this angle over here, we can call it Z.
- So, these two combined are gonna add up to 90 degrees
- or Z is going to be equal to 58 degrees.
- And now we're inside the triangle that we care about
- to figure out theta, we already figured out earlier on this video.
- Well this is 58 degrees, if this over here is 90
- then this one over here is also going to be 90
- because they are supplementary.
- So you have 58 degrees, you have 58 degrees
- I wanna do that orange color.
- So, if you have 58 degrees plus this 90, plus 90 plus theta now
- plus theta now is going to be equal to 180 degrees.
- You can subtract 90 from both sides, that becomes 90
- and you have 58 plus theta is equal to 90 subtract 58 from both sides
- you get theta is equal to 32 degrees again.
- And so we got the same answer.
- I just wanna do that, to show you that there are multiple ways
- to do this problem, and as long as you're doing things
- that are logically consistent you're making assumptions
- that you can make and then logically deducing step by step,
- there's multiple ways to get that right answer.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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