# Trapezoid and rhombus relationship problems

### Quadrilateral properties (video) | Shapes | Khan Academy

Problem 29RQ: The Venn diagram shows the relationships among polygons Thus a square is a quadrilateral, a parallelogram, a rectangle and a rhombus. Draw a Venn diagram that shows the relationships among quadrilaterals, trapezoids, parallelograms, rhombuses,. Solutions for Chapter Problem 10LA. A trapezoid has one pair of parallel sides and a parallelogram has two pairs of the relationship between trapezoids and parallelograms for each definition? K- 6 Geometry Progressions document for more information about these issues.

So the first name in question is a quadrilateral. And a quadrilateral is literally any closed shape that has four sides. And this is definitely a closed shape that has four sides.

So it is definitely a quadrilateral. Next, we have to think about whether it is a parallelogram. A parallelogram is a quadrilateral that has two pairs of parallel sides, where in each pair they're opposite sides.

### Illustrative Mathematics

And in this case, if you look at this side over here, it forms a degree angle with this line. And this side over here also forms a degree angle with this line over here.

So these two sides are parallel. And then you could make the exact same argument for the other two sides.

### Quadrilateral - Wikipedia

This line up here forms a degree angle with this side. And so does this side. It forms a degree angle with this line right over here. They form the same angle with this line. So this side is parallel to that side right over there.

So this is definitely also a parallelogram. Next, we ask about a trapezoid. Now, trapezoid is interesting. Sometimes a trapezoid is defined as any quadrilateral having at least one pair of parallel sides.

Sometimes it's defined as having only one pair of parallel sides. So let me write this down. Trapezoid, there's a debate here. It's not completely settled. Some people say at least one pair of parallel sides. That's one definition, one possible definition. The other one is at exactly one pair of parallel sides.

How we answer this question depends on which definition for trapezoid we pick. Now, the one that people most refer to is actually this one right over here, exactly one pair of parallel sides. So when you think of a trapezoid, they think of something like this, where this side over here is parallel to that side over here and those two are not parallel.

But sometimes you'll also see this at least one pair of parallel sides. And so this would include parallelograms.

It would be inclusive of parallelograms because parallelograms have two pairs of parallel sides. But I'm going to go with this definition right over here, exactly one pair of parallel sides. In other words, parallelograms include all rhombi and all rhomboids, and thus also include all rectangles.

An equivalent condition is that the diagonals perpendicularly bisect each other.

**rectangle(आयत) rhombus (समचतुर्भुज) trapezium (समलम्ब चतुर्भुज) part 5 of mensuration**

Not all references agree, some define a rhomboid as a parallelogram which is not a rhombus. An equivalent condition is that the diagonals bisect each other and are equal in length. Rectangles include squares and oblongs. An equivalent condition is that opposite sides are parallel a square is a parallelogramthat the diagonals perpendicularly bisect each other, and are of equal length.

## Quadrilateral

A quadrilateral is a square if and only if it is both a rhombus and a rectangle four equal sides and four equal angles.

This implies that one diagonal divides the kite into congruent trianglesand so the angles between the two pairs of equal sides are equal in measure. It also implies that the diagonals are perpendicular.

A convex quadrilateral is tangential if and only if opposite sides have equal sums. It is a type of cyclic quadrilateral. A Watt quadrilateral is a quadrilateral with a pair of opposite sides of equal length. A dart or arrowhead is a concave quadrilateral with bilateral symmetry like a kite, but one interior angle is reflex.