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[Core] Quadrilateral Question

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Quadrilateral Question

關於quadrilateral諗唔到點做
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Did you have any progress? Here are some small hints.

Q1 is interesting. If you redraw the diagram yourself with the conditions given, the line segment GF is not fixed. You can move it horizontally however you want! To see what I mean, here's a figure for you to play around.
https://www.desmos.com/calculator/ncde1is2pz?lang=zh-TW (Spoiler: There is a big hint in it)
This should give you some inspiration to prove it.

Regarding Q2, I wonder how much have you worked on it, because a lot of people who just started learning deductive geometry don't label (almost) ALL the information from the given. After labeling, you should be able to complete the proof. As with a lot of geometry problems, looking out for parallel lines is always a good start.
(Note on Q2: The diagram is misleading as per usual. Do NOT assume any right-angle-lookalikes as right angles.)

If you want a complete solution, respond here (and preferably PM me), because I'm bad at LaTeX...

EDIT:
After many hours struggling with LaTeX, here's a solution for both questions.
https://www.docdroid.net/9Q77tKx/geometry-pdf
Note 1: I really suggest you don't copy my work yet, unless you still can't solve the problems with the hints given.
Note 2: I tend to be long-winded with proofs.
Note 3: Oops, there's a minor mistake in Q2. However you should be able to spot it.

[ 本帖最後由 風之男 於 2020-10-4 10:45 PM 編輯 ]

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