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What is the proof that the α angles are equal? I can see that the lower and middle angles are equal because they are "alternate interior angles". I can deduce that the middle and upper angles are equal too, but how do you express it formally?

https://i.stack.imgur.com/81sHd.png

Thanks in advance.

Chris Shiherlis
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  • I like to think that my version of a proof makes things a little more clear. – Blue Oct 13 '19 at 21:32
  • Welcome to Math.SE. Can you please [edit] your post and write your attempts at solving the problem? If your question is clear and focused on your specific difficulty and you show your effort in solving the problem, it's more likely to get good and helping answers. By the way, take the opportunity to take the [Tour], if you haven't done it already. See also some tips on [ask], on formatting help and on writing down equations using LaTeX / MathJax. – Ertxiem - reinstate Monica Oct 13 '19 at 21:32

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The angle $\alpha$ in the middle on the right is equal to the bottom left angle $\alpha$ since alternate angles are equal. There is a right angle at the blue dot, so the angle next to $\alpha$ here must be $\pi/2-\alpha$. Then use the right-angled triangle in the top right.

A. Goodier
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