In the figure above, SQRE is a square and AB = AC.

[ajaym8]

hi,
we're going to need to see the figure to address these questions. can you please post the figure (and/or post it on an image-hosting website and put a link here)?

thank you.

Sure. Please find the link below.

https://i.imgur.com/KYtdnvO.png

Thanks,
Ajay

[RonPurewal]

thanks for posting the image.

are we saying that due to symmetric placement of the triangle, CE=BR?

^^ yes, that's exactly what we are saying.

• a square (like any other rectangle) has left-right symmetry.

• according to statement 2, the top of the triangle is placed EXACTLY in the middle of the square.
• the triangle is isosceles (AB = AC), from the original statement.
...from these two statements together, we know that the ENTIRE FIGURE has perfect left/right symmetry -- i.e., anything that happens on the left side, also happens (in mirror image) on the right side.

• ...so, yes, CE and BR have the same length.

[GabrielaM951]

I thought I needed to know if this triangle was a right triangle so I can know if the Base is CB or CA. Why that's not necessary?
Depending on if it's a right triangle the formula can be:
CAxCB/2 or CBxh(side of the square)/2

[RonPurewal]

^^ the second of those formulas definitely works (because CB is coincident with a side of the square). so, it's irrelevant whether the other one might also work.