Question

Consider the graph of quadrilateral ABCD.


What is the most specific name for quadrilateral ABCD?

square
rectangle
parallelogram
rhombus

Answer 1

I don’t see the graph. Could you post the picture or the coordinates of A, B, C, D?

If you can’t, here’s how to decide from a graph or coordinates:

1. Check parallel opposite sides (parallelogram test)
- Compute slopes: slope(AB) and slope(CD); slope(BC) and slope(AD).
- If slope(AB) = slope(CD) and slope(BC) = slope(AD) then ABCD is at least a parallelogram.

2. Check for right angles (rectangle test)
- For adjacent sides use slopes or vectors. If slope(AB) · slope(BC) = −1 (or vector dot product = 0) then angle B is 90°.
- If all four angles are right angles (or two adjacent are right in a parallelogram), it’s a rectangle.

3. Check for equal side lengths (rhombus test)
- Compute distances |AB|, |BC|, |CD|, |DA|.
- If all four are equal it’s at least a rhombus.

4. Combine:
- If it’s a parallelogram with all sides equal → rhombus.
- If it’s a parallelogram with all angles 90° → rectangle.
- If it has all sides equal and all angles 90° → square (most specific).

So the most specific name among your choices is:
- square if both conditions (all sides equal and right angles) hold,
- otherwise rectangle if only all angles are 90°,
- otherwise rhombus if only all sides are equal,
- otherwise parallelogram if only opposite sides are parallel.

Send the graph or coordinates and I’ll classify ABCD exactly.