ABCD is a quadrilateral.
AB=CD
Angle ABC = angle BCD
Prove that AC = BD

compare the triangles ΔABC and ΔBCD

∡ABC = ∡BCD (given)

AB = CD (given)

BC = BC (common)  } = > (SAS) ΔABC ≡ ΔBCD = > AC = BD

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

i believe your answer is 99.7% of 7-year-old children are between 46.6 inches and 49.5 inches tall.