To a first approximation, they describe the match or mismatch between a person's gender identity and their assigned gender at birth (AGAB).

"Cis" = "my gender identity matches my assigned gender at birth"
"Trans" = "my gender identity does not match my assigned gender at birth"

The question being asked is, "Given that when you were born they thought of you as a (boy/girl); are you now expressing or experiencing a (male/female) gender, or a (female/male) one?"

Logically speaking, this is an xor operation; it asks if two things are the same or different. If boolean variable a represents your AGAB and boolean variable b represents your gender identity, then "are you trans?" is a xor b — is your AGAB different from your gender identity?

Again, this is to a first approximation. There are people who don't fit binary labels, and so an xor operation on binary labels doesn't fit them either.

Cis and trans are terms that came before their application to gender identity. I learned themin organic chemistry in reference to chemical isomers.

Wikipedia: The prefixes "cis" and "trans" are from Latin: "this side of" and "the other side of", respectively.

As applied to gender, "this side of" you are the gender of the sex you were born as. "The other side of" means you have switched your gender to the other side of the sex from which you were born.

Edit: to answer your question more directly, your gender is cis or trans of the sex you were born as. The question you ask for is: "is your gender cis or trans of your sex?"

Please note I’m typing this as a trans man. Being “cis” or “trans” stems from someone’s gender.

Basically, do you identify as your birth gender (not sex, gender and sex are different)? If the answer is yes, you are “cis”. If the answer is no, like I my case, I was born female, I identify as a male, then you are are trans.

I hope this answers your question.

I think the confusion is coming from the fact that cis and trans really only have context of an expectation. In this case, it would be the expectation of society.

You are correct that if you identify as a woman or a man, you are a woman or man. If you have a penis, or a vagina, or some mix or lack of those, then those are just parts of your body and that isn't really up to interpretation.

In broad strokes, society expects your body parts (penis, vagina) to correspond to how you identify (man, woman). Humans are kind of just built this way. Our brains take a lot of shortcuts and categorize the world around us. It is statistically likely that if you have a penis, you identify as a man.

As we've evolved as a society, we have come to understand and recognize that these statistically likely correlations not always hold up (it's just likely, not a guarantee, after all). So cis and trans are descriptors of whether or not the correlation between your gender identity and your physical characteristics match (cis) or don't match (trans) society's expectations.

I'm male, I look in the mirror and see a man, I'm fine being a man. I'm gay, I've pondered 'but what if I was a woman'? My body, clothing, etc. ... Nahh, that's not me. I'm cisgendered.

'cis' means, metaphorically, 'same side'. cis- is a prefix used in other disciplines, and was first used in 1914. It's not a 'made up woke word' like bigots claim.

Also, all words are made up. We make language work for us, and it changes all the time. This is a feature not a bug.

Cisgender means the person has a gender identity that matches the sex they were assigned at birth.

If you are a man and you were assigned male at birth, you are cis.

If you are a man and you were assigned female at birth, you are trans.

Non-binary can mean anything from not having a strong specifically male or female identity to closer to switching identities (bi-gender falls closer into this) to just having a lot of serious fluidity, but typically speaking at least part of the time the identity doesn’t match the assigned sex at birth.

gender chirality . gender isomerism. gender topology

I don't think any of you read his question.

They're adjectives. Just like "tall" or "smart" or "young".

The question would just be "are you cis or trans?", there's not a specific word or term that you'd use.

You can think of 'cis' and 'trans' as meaning roughly 'this side' and 'other side'.

In a gender context the 'sides' are male and female and the items are physical gender and mental gender. If both genders are on the same side, both on 'this side', that's 'cis'. If they are different, one 'this side', one 'other side', that's 'trans'.

So, if the answer is "I am cis/trans" the question is "Is your mental gender the same as your physical gender?" "I am cis" then means "My mental gender is the same as my physical gender" and "I am trans" means "My mental gender is not the same as (or maybe 'is opposite') my physical gender".

Note that 'physical gender' is not always clear. Some people are born with ambiguous genitalia and may be surgically altered to make their genitalia more closely resemble the commonly recognized pattern for 'male' or 'female', and some may be left as-is. In some cases this can be a reason for a trans gender identity.

"Describe the relationship between your assigned gender and your gender identity."

I think it's an alignment, like parallel vs. perpendicular.

If you identify with your sex at birth, whatever it is, your identity is aligned with your biological sex at birth, that is called Cisgender. Parallel.

If your gender identity is not aligned with your biological sex at birth, it is at an angle to it, perhaps perpendicular (you were a boy baby but are a woman) perhaps a different angle (perhaps were born a girl and are non-binary). Anything other than that parallel alignment is thrown into the Trans bucket, but particularly the perpendicular arrangements.