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In order to prove AC perpendicular to BD, you just have to prove that the triangles inside the parallelogram are right angle triangles.

You have to use the angle property of a parallelogram which says: The interior opposite angles are equal. But more importantly, the sum of adjacent angles in a parallelogram = 180.

Ref

Since AC bisects BCD, let’s call angle ECB as x. So angle ECD is also x

Similarly let’s call the bisected angle of ABC as 2y, therefore EBC = EBA = y

Now we know that 2x+2y=180 (referenced above) Now it’s just simple algebra. Dividing the equation above by 2, you get: x+y=90.

So angle ECB + angle EBC = 90. So in the triangle BEC, you have the sum of 2 angles as 90. Remember the rule of triangles? The sum of all the angles of a triangle result in 180. Therefore the only logical explanation is that the remaining angle BEC should be = 90. Which means that AC has to be perpendicular to BD

Hi, my proof options were a bit different because it wont allow me to use algebra as a reason. For example it would be like, "only select vertical angles, cpctc, angle bisector etc." My options were this attached picture below.

Also XY and all those variables are just there as a placeholder, you would have to change those.

https://snipboard.io/fXCpNl.jpg

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I don’t quite follow. Do you have to choose one of the options? Or are those sequences in the proof? I mean you are right, none of them seem to make sense.

The only statement I would say is angle X is a right angle lol.

You have to choose one of those options and change it and they are not in the proof. I made a video here so that you know what I am talking about:

https://www.youtube.com/watch?v=rv_wENeIyYc

Oh I see.

My guess would be that the angle X and angle Y are complementary Can you post the second set of options for that option? I only see the first set in your image.

So is this related to some traffic configuration in Massachusetts or something?

Those were all the options.

i am gonna delete this or something