Hi, I’m not sure how to solve this

[gilded sail]

!showwork

[dapper bear]

Show your work, and if possible, explain where you are stuck.

[primal shuttle]

Oh um, I don’t know how to “Prove: 1/2 quad ABCD=quad PQRS”

I don’t know what steps to take to prove that

[gilded sail]

you have to look into

1. what you've learnt (what's the context of your question? where does it appear?)
2. what (conditions in the question) can you see?
3. how can you link them up?

[gilded sail]

this is a textbook problem of the famous "linearity of signed area" mentioned in https://math.stackexchange.com/a/4437156/290189

to make your problem solving process and product organized
i suggest the Zhang Jingzhong (張景中)'s Elimination Point method (消點法)
https://media.discordapp.net/attachments/486841085210132490/968248935682551858/unknown.png

a "constraint point" is a point under some constraint (from the question)

you pick the "final construct point" (based on the construction order)
and eliminate it first (from known geometric principle), so that it "vanish"

from your target geometric quantity

you don't need to hesitate which point to eliminate, and it's possible to program a machine to solve it
that's why you see at the bottom line of the above screen cap, it says "mechanical theorem proving"

[unborn sigil]

Omg

I rmb doing the exact same question when I was grade 9

I think I used sth like "mid-point theorem" to prove this

I actually got stuck for a while too

[unborn sigil]

I kinda forget how but I rmb using this a few times to prove it

[primal shuttle]

Thank you both, I apologize for my late response I thought I wasn’t going to get one 💀

I appreciate your help