i cant prove part(b). i think since ABCD is rectangle and not square, Ab is not equal to BC. this means the two triangle cannot be the same.pls help me thanks

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take the two triangles ABC and the triangle PBQ we have

AB = PB cuz ABP equilateral triangle
BC = BQ cuz BCQ equilateral triangle and
<ABC = < PBQ = 90

the two triangles congruent with SAS side-angle-side in the result you have
AC=PQ

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A rectangle may be square; it may have equal sides.
A square can ONLY have equal sides.

A square is included in the definition of rectangle.

draw AC and PQ
angle ABC = angle PBQ = 90
AB = CB
PB = QB
hence triangle ABC congruent PBQ (SAS)
hence AC = PQ

sorry...mistake:
AB = PB
CB = QB