Answer: Choice D) All rhombuses are squares
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Explanation:
Let's go through the answer choices to see which are true and which are false.
- A) This is a true statement since all squares have all four angles of 90 degrees each. Any square is a rectangle, but not the other way around. We can cross choice A off the list.
- B) This is also a true statement. The opposite sides of a rectangle are parallel, which by definition makes it a parallelogram. Any rectangle is a parallelogram, but not the other way around. Cross choice B off the list.
- C) Yet another true statement. Parallelograms have four sides, which means they are quadrilaterals. Cross choice C off the list.
- D) This is false. Yes some rhombuses are squares, but others are not. A rhombus has all four sides the same length. If all four angles were 90 degrees each, then we'd have a square. But if the rhombus has its angles that aren't 90 degrees, then we have a non-square rhombus. Any square is a rhombus, but not the other way around.
Check out the venn diagram below showing the connection between the geometric shapes mentioned. The large outer rectangle represents the set of all quadrilaterals. Inside this is the oval representing all parallelograms. Then inside the oval is the set of rectangles and the set of rhombuses. The overlapping region of the rectangles and rhombuses is the set of squares, marked in blue.
As you can see, picking any square will get us a rhombus and a rectangle automatically. However, picking any rhombus will not guarantee it's a square.
