Question

a quadrilateral with congruent diagonals must be a(n)
square
rhombus
isosceles trapezoid
rectangle
no classification guaranteed
question 3
a quadrilateral can have exactly 3 right angles.
true
false

Explanation:

• For the first question:
• A square has congruent diagonals, but so do rectangles and isosceles trapezoids. A rhombus has diagonals that are perpendicular bisectors of each other but not necessarily congruent. Just because a quadrilateral has congruent diagonals does not guarantee it is a square, rectangle, or isosceles trapezoid. For example, a non - regular quadrilateral can be constructed with congruent diagonals that is not a square, rectangle, or isosceles trapezoid.
• For the second question:
• The sum of the interior angles of a quadrilateral is \((4 - 2)\times180^{\circ}=360^{\circ}\). If there are three right angles (\(90^{\circ}\) each), the sum of those three angles is \(3\times90^{\circ} = 270^{\circ}\). Then the fourth angle is \(360^{\circ}-270^{\circ}=90^{\circ}\). So a quadrilateral cannot have exactly 3 right angles.

Answer:

• First question: No classification guaranteed
• Second question: False