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In any cyclic quadrilateral, any two opposite sides are antiparallel with respect to the other two sides. Lines l 1 {\displaystyle l_{1}} and l 2 {\displaystyle l_{2}} are antiparallel with respect to the line m {\displaystyle m} if they make the same angle with m {\displaystyle m} in the opposite senses.
Like a parallelogram, an antiparallelogram has two opposite pairs of equal-length sides, but these pairs of sides are not in general parallel. Instead, each pair of sides is antiparallel with respect to the other, with sides in the longer pair crossing each other as in a scissors mechanism. Whereas a parallelogram's opposite angles are equal ...
The solutions with four congruent tiles include some with five sides. [2] However, their placement surrounds an uncovered hole in the plane. Among solutions without holes, the ones with the fewest possible sides are given by a hexagon identified by Scott Kim as a student at Stanford University. [1]
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One side (left in the illustration) is partially folded in half and pinched to leave a mark. The intersection of a line from this mark to an opposite corner (red) with a diagonal (blue) is exactly one third from the bottom edge. The top edge can then be folded down to meet the intersection. [4]
For every concave kite there exist two circles tangent to two of the sides and the extensions of the other two: one is interior to the kite and touches the two sides opposite from the concave angle, while the other circle is exterior to the kite and touches the kite on the two edges incident to the concave angle. [28]
Yesterday we saw PSI in the puzzle, clued as [Second-to-last Greek letter]. SANS (51D: Without, in French) This makes me think of SANS-serif fonts, fonts in which the letters are without serifs ...
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