P.S I've noticed that I have been struggling with proof questions and was wondering if anyone knew how to get better at them? Thanks!
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I know ArtyDreams has given you a headstart on the question but I thought I'd chuck in my two cents as well so that you can see how I would go about setting up a proof. Hope it's some help!
For proofs, my method was to write down all the things I
know (the information in the question). For the question you've attached that would mean writing down AB=BC=CD=DA and AB=AX=BX.
Then you could also write down that as ABX is equilateral angles ABX, BAX and AXB are all 60 degrees. Because of this XBC and XAD are 30 degrees (due to the corners of a square being 90 degree angles).
As triangles AXD and BXC are isosceles (as AX=AB=DA and BX=AB=BC) angle ADX must be equal to AXD. Angle BXC must be equal to BCX. those angles are (180-XBC)/2. They are (180-30)/2 or 75 degrees each.
Then I would down what I have to
show. This question doesn't ask you to prove anything, but if you wanted to prove that angle DXC is 150 degrees I would actually write that at the top of the page before I start my proof.
Then I would use the things from the "
know" section to actually complete the proof.
My Proof Layout
SHOW: DXC = 150
LHS = DXC
= 360 - AXB - AXD - BXC
= 360 - 60 - 75 -75
= 150 = RHS as required
Best of luck!