1. does py=pz? 2. is pb> py? 3. must the slant height be greater than the altitude? 4. can all edges have the same length? 5. given the regular square pyramid with rs=6 and px=4 then xy=3 true or false? 6. given a regular square pyramid with rs=6 and px=4 find pya. 5b. 5 square root 3c. 6

PY = PZ is true.

Step-by-step explanation:

We are given a figure of a regular square pyramid and we are to determine whether PY is equal to PZ or not.

From the figure, we can see that ∠PXY and ∠PXZ are right angles and since the base is a square so sides AB and BC are equal in length and Y and Z are their mid points respectively.

Therefore, the hypotenuses created by PY and PZ are equal.

Check the picture below.

all slant-heights are the same in a square pyramid, so yes, PY = PZ.

if you notice in the picture, the green line is longer than the black dashed line, now, we're using some values for the sake of examplifying, so the side at the base for the slant-height is shorter than the the side at the base for the corner of the pyramid, and therefore PY > PB.

must the slant-height be greater than the altitude?  well, notice on that yellow triangle, the slant-height is the hypotenuse and the hypotenuse is always greater than the other sides in a right-triangle.

could the edges be the same length?  well, we can squeeze that well for the base sides and the slant-heights, but we can't for the corners, the corners must always be longer than the slant-heights, so nope.

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step-by-step explanation:

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