Shared by a Veda teacher · Generated with Veda AI · Oct 2026
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. Here's a taste from this kit; the app has the full deck.
Four sides is not a definition
Join any four points in order and you may get a figure with three corners in a line, a figure that never closes, a figure whose sides cross, or one whose corners will not lie flat. All four have four sides.
The definition in one sentence
Take four distinct points in a plane and join them in order by four segments. The figure is a quadrilateral provided every point on it, apart from the four corners themselves, lies on exactly one of those segments.
Three things to check
The one sentence hides three separate requirements. All four corners lie in a single plane. No three of the corners lie on one straight line. And no non-corner point of the figure belongs to two sides.
Parallel is the definition
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. That, and nothing else, is the definition.
Opposite sides are equal
Draw a diagonal. It is a transversal for both pairs of parallel sides, so two pairs of alternate angles are equal, and the diagonal itself is common to the two triangles.
Adjacent angles add to 180
Opposite angles of a parallelogram are equal. The more useful way to say the same thing is that ADJACENT angles are supplementary.
Four straight sides is not a definition: it lets in figures with three corners in a line, figures that never close, figures whose sides cross and figures that will not lie flat. The precise rule asks for four coplanar ve…
~40 min · full explanation, examples & memory tricks in the app
A parallelogram is defined by having both pairs of opposite sides parallel; equal sides, equal opposite angles and bisecting diagonals are consequences. Reversing each of those three gives a true converse, and with the e…
~45 min · full explanation, examples & memory tricks in the app
The segment joining two midpoints of a triangle is parallel to the third side and half its length, which cuts a triangle into four congruent pieces, puts the centroid two thirds of the way along every median, and makes t…
~50 min · full explanation, examples & memory tricks in the app
174 questions laddered from warm-up to topper-level, each with an explanation. A taste:
TRIM is drawn by joining four points in order, but three of those points turn out to lie on one straight line. Which requirement of the definition does TRIM fail?
Beginnerno three of the four vertices may be collinear
When three vertices share a line, the two sides meeting at the middle one lie along that same line, so the figure collapses towards a triangle instead of enclosing a four-sided region.
The four corners of TILT cannot be laid flat on a single sheet of paper. TILT is best described as
Beginnera non-planar 4-gon
Four-sided figures whose vertices do not share a plane are called non-planar. They are genuine objects, but this chapter studies only the planar ones.
In BOWS the side joining the first and second corners crosses the side joining the third and fourth. BOWS is
Beginnerself-intersecting
At the crossing point there is a point of the figure, not a vertex, that sits on two different sides at once. The definition allows such a point on exactly one side, so BOWS is excluded unless we deliberately call it self-intersecting.
In quadrilateral ABCD, the two segments AC and BD are its
Beginnerdiagonals
A diagonal joins two vertices that are not next to each other. AC skips B and BD skips C, so these are the two diagonals rather than sides.
60 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
The full Veda Bites deck, complete notes, spaced-repetition flashcards, leveled MCQs, tests and games for this kit — plus Daily Facts and the Arena, every day.
