Question

the following biconditional true? a quadrilateral is a rectangle if and only if it has at least three right angles. yes no

Explanation:

Step1: Recall the properties of a rectangle

A rectangle is a quadrilateral with four right angles.

Step2: Analyze the sum of interior angles of a quadrilateral

The sum of interior angles of a quadrilateral is \(360^{\circ}\). If a quadrilateral has three right angles (each \(90^{\circ}\)), the fourth angle is \(360 - 3\times90=90^{\circ}\). So, a quadrilateral with at least three right angles has four right angles.

Step3: Check the biconditional

If a quadrilateral is a rectangle (by definition four right angles), it has at least three right angles. If a quadrilateral has at least three right angles (proven to have four right angles), it is a rectangle.

Answer:

yes