Question

is the following conditional true? if a quadrilateral has at least three right angles, then it is a rectangle. yes no

Explanation:

Step1: Recall angle - sum property

The sum of interior angles of a quadrilateral is $360^{\circ}$.

Step2: Analyze the case of three right - angles

If a quadrilateral has three right - angles, each right - angle is $90^{\circ}$. Let the three right - angles be $\angle A = 90^{\circ}$, $\angle B=90^{\circ}$, $\angle C = 90^{\circ}$. Then, by the angle - sum property of a quadrilateral $\angle A+\angle B+\angle C+\angle D=360^{\circ}$. Substituting the values, we get $90^{\circ}+90^{\circ}+90^{\circ}+\angle D = 360^{\circ}$, so $\angle D=360^{\circ}-(90^{\circ}+90^{\circ}+90^{\circ})=90^{\circ}$. A quadrilateral with four right - angles is a rectangle.

Answer:

yes