Question

complete the sentence. quadrilateral abcd must be a rectangle if ∠a≅∠b≅∠c≅∠d ab = cd and ad = bc m∠a + m∠b = m∠c + m∠d = 180°

Explanation:

Step1: Recall rectangle properties

A rectangle has four right - angles. In a quadrilateral, if all angles are congruent, since the sum of interior angles of a quadrilateral is 360°, each angle is 90°.

Step2: Analyze each option

• For $\angle A\cong\angle B\cong\angle C\cong\angle D$, let the measure of each angle be $x$. Then $4x = 360^{\circ}$, so $x = 90^{\circ}$. A quadrilateral with four right - angles is a rectangle.
• For $AB = CD$ and $AD=BC$, this makes the quadrilateral a parallelogram.
• For $m\angle A + m\angle B=m\angle C + m\angle D = 180^{\circ}$, this only shows that adjacent angles are supplementary, which is true for all parallelograms.

Answer:

$\angle A\cong\angle B\cong\angle C\cong\angle D$