No, it can be a triangle intersecting a set of three faces which meet at one vertex.
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The diagonals of a rectangular shape will only bisect opposite angles if, in fact, the shape is a square. Otherwise they will not bisect them.
No, a rectangular prism's cross-section will always have between 1 and 4 (inclusive) straight lines only.
Just remember- The opposite sides are ALWAYS equal.
yes, because perpendicular lines always intersect. all lines intersect unless they are parallel or on separate planes (skew)
No. Lines can intersect at any possible angle.