The Alternate Segment Theorem Explained

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The Alternate Segment Theorem Explained | Maths GCSE

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A quick example of solving a circle theorem question to help with your maths GCSE revision!
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Пікірлер: 58

@revisionboost 11 ай бұрын

The best way to revise: www.revisionboost.com/gcse-maths/

@aayushixi 10 ай бұрын

ahh finally a short and sweet explanation! thanks!

@revisionboost 10 ай бұрын

Glad it helped!

@olaniyanoluwakemi9763 Жыл бұрын

Wow this is so explanatory. Thank you sir

@ryze3024 3 ай бұрын

You can also use the external angle theorem of a triangle.

@THERHINOFORZA4 3 ай бұрын

Tf is that

@paulbushey9409 3 ай бұрын

The sum or the 2 remote interior angles = the exterior. However, notice that the angle in question is smaller than the exterior angle.

@Dog-id2zx 2 ай бұрын

Alternate is so much easier. Its one step.Idk why he's making it so confusing

@AiRenwick 8 ай бұрын

Ha me knowing the awnser before he even spoke, yha this take me back to my school years, also the awnser is x=60°,but i never remembered the reason 😂

@emilyballesteros6400 7 ай бұрын

Because the intercepted arc is twice to it's inscribed angle

@emilyballesteros6400 7 ай бұрын

Because the intercepted arc is twice to it's inscribed angle

@AiRenwick 7 ай бұрын

Yes but back in my day we had a verry specific sentence to wright and in a different language so i can't really say if this is correct but thanks

@ShriNiwas-eu8xf 5 ай бұрын

Will u provide proof of this theorem??

@oogaboogaaspire 2 ай бұрын

he just did

@ShriNiwas-eu8xf 2 ай бұрын

@@oogaboogaaspirereally??

@SilentFortissimo 7 ай бұрын

Thank you so much! I finally understood it 😊

@paulbushey9409 3 ай бұрын

this is the alternate segment theorem. It’s pretty easy to prove, just extend two sides of that triangle (the chords) and you can see the triangle exterior angle theorem at work. Add the three angles together and get 180° as it should be. Kind of hard to explain without a picture.

@bananbanan98 2 ай бұрын

I solved it before I watched the video, safe to say your explanation was much simpler, but I still got it right.

@yithenntan7875 6 ай бұрын

Are the red lines supposed to touch the end of that chord? To be precise.

@revisionboost 6 ай бұрын

That's right!

@noahcosijns7318 8 ай бұрын

I solved it in a different way! If you construct a line which intersects with the tangent point at a rigt angle, you'll get a side of a triangle which goes through the middle. Use the chord mentioned in the video as a 2nd side to the triangle and simply connect for the 3d. We now know one of the angles is 90° - 60° = 30°. Furthermore, the opposite angle of that line we constructed is 90°. This can be proven quite easily, as the angles opposite to a chord are all equal and we can construct a 90°, 45°, 45° triangle. So we now have 90°, 30° and x. Therefore x must be 180° - 90° -30° = 60° I solved it this way since I was not yet aware of the 2nd theorem you used. However, my solution to this problem can easily be adapted into a proof for said theorem.

@ssjgamerz4900 7 ай бұрын

bhbai wo is theorem ka hi proof h

@ABX_PYQ 7 ай бұрын

you explained so well It was helpful to me Love from india ❤

@bhaveshchoudhary5049 6 ай бұрын

Explanation is perfect but i like that paper very much on which you are explaining the theorem 😂😂😂😂

@AmenMulatu 8 ай бұрын

When you go to the movies, you want to be close to the movie screen, but you don't want to have to move your eyes too much to see the edges of the picture. If E and G are the ends of the screen and are at F, m(EFG) is called your viewing angle. You decide that the middle of the sixth row has best viewing angle. If someone is sitting there, where else can you sit to have the same viewing angle? Find whatever‘ it is

@user-oo2qq6mo2w 11 ай бұрын

Can I say that interior angles are equal to the opposite exterior angle

@UnveilingTheUnspoken62 11 ай бұрын

No, in a triangle inscribed in a circle, the interior angle is not necessarily equal to the opposite exterior angle. In fact, the sum of the measures of the two interior angles opposite each other in the triangle is always equal to the measure of the exterior angle formed by the third side of the triangle. This is known as the Exterior Angle Theorem. So, the interior and exterior angles are related, but they are not necessarily equal🙂

@revisionboost 11 ай бұрын

Unfortunately not!

@RichardAwuah-my8xz 2 ай бұрын

@MohammedNobi-fs7uj Жыл бұрын

Much better

@user-qr9ne3mq6e 5 ай бұрын

X is 60 because 180 ➗ by 3 sides that equals to 60 that so much easier to understand

@feminico2613 5 ай бұрын

it won't always be 60 degrees, what if the angle is 30 degrees? It wouldn't work anymore wouldn't it

@akshat9502 7 ай бұрын

Thanks a lot, Sir. I had a hard time understanding it. 😢😢

@jozitro4554 7 ай бұрын

No protractor... Minus 11 points.

@ayesha904 6 ай бұрын

Are these alternate angle is similar to similarity

@alialyanalyan6375 4 ай бұрын

finding this right after the test, just my luck 🙂

@CherryBomber15 11 ай бұрын

why is x 60?

@revisionboost 11 ай бұрын

Because of the alternate segment theorem!

@mikethegamedev 9 ай бұрын

did you even watch the video

@yoshikagekira4938 10 ай бұрын

The only thing I noticed is how you write x

@ZamanSidheequeHishamPallath 10 ай бұрын

Does all the angles in a triangle equal to the angle at Chord or just one

@revisionboost 10 ай бұрын

Normally just one of them!

@lior_shiboli 8 ай бұрын

Usually just but if it happens and they all have the same angle then they all have an angle of 60 always(for that you need all the sides to be equal as well)

@badphysiotdx2395 11 ай бұрын

Cheers

@thakgatsomashego777 8 ай бұрын

Tan-chord theorem?

@nega_popo 4 ай бұрын

alternate segment theorem

@-Hellow- 8 ай бұрын

What is the proof for this though?

@sigmamate8 3 ай бұрын

is this a higher tier question?

@user-zg1ww1jn7f 3 ай бұрын

@sigmamate8 3 ай бұрын

@@user-zg1ww1jn7f who are you to tell me

@tantffg9119 10 ай бұрын

What is a chord

@revisionboost 10 ай бұрын

A line that passes through a circle without passing through the center :)

@lior_shiboli 8 ай бұрын

Ah yes, proof by "its a theorem"

@scptime1188 8 ай бұрын

....yeah? if mathematicians had to prove every theorem they cite in proofs nothing would ever get done lol. a theorem is a provable statement based on a set of axioms.

@lior_shiboli 8 ай бұрын

@scptime1188 I mean I know, but I meant that tye theorem is just the question

@SenileLuke 8 ай бұрын

@@scptime1188yeah, but instead of saying “this theorem says so” instead they should explain the proof of the theorem. If they can…

@ow7398 8 ай бұрын

@@SenileLukeyou can prove the alternate segment theorem by drawing a line from the tangent point (at the bottom) to the centre of the circle, and then another line from the centre of the circle to the other point of the triangle (on the top right) to make an isosceles triangle