### All PSAT Math Resources

## Example Questions

### Example Question #241 : Geometry

Quadrilateral *ABCD* contains four ninety-degree angles. Which of the following must be true?

I. Quadrilateral *ABCD* is a rectangle.

II. Quadrilateral *ABCD* is a rhombus.

III. Quadrilateral *ABCD* is a square.

**Possible Answers:**

II and III only

I, II, and III

I only

II only

I and II only

**Correct answer:**

I only

Quadrilateral *ABCD* has four ninety-degree angles, which means that it has four right angles because every right angle measures ninety degrees. If a quadrilateral has four right angles, then it must be a rectangle by the definition of a rectangle. This means statement I is definitely true.

However, just because *ABCD* has four right angles doesn't mean that it is a rhombus. In order for a quadrilateral to be considered a rhombus, it must have four congruent sides. It's possible to have a rectangle whose sides are not all congruent. For example, if a rectangle has a width of 4 meters and a length of 8 meters, then not all of the sides of the rectangle would be congruent. In fact, in a rectangle, only opposite sides need be congruent. This means that *ABCD* is not necessarily a rhombus, and statement II does not have to be true.

A square is defined as a rhombus with four right angles. In a square, all of the sides must be congruent. In other words, a square is both a rectangle and a rhombus. However, we already established that *ABCD* doesn't have to be a rhombus. This means that *ABCD* need not be a square, because, as we said previously, not all of its sides must be congruent. Therefore, statement III isn't necessarily true either.

The only statement that has to be true is statement I.

The answer is I only.

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