Question

question
choose all answers that describe the polygon ( tuvw ) if
( overline{tu} cong overline{vw}, overline{uv} cong overline{wt} ), and
( mathrm{m} angle t=mathrm{m} angle u=mathrm{m} angle v=mathrm{m} angle w ).
answer
parallelogram
quadrilateral
rectangle
rhombus
square
trapezoid

Explanation:

Step1: Analyze the number of sides

A polygon with four vertices (T, U, V, W) is a quadrilateral.

Step2: Check for rectangle properties

Since \(m\angle T=m\angle U = m\angle V=m\angle W\), and the sum of interior angles of a quadrilateral is \(360^{\circ}\), each angle is \(90^{\circ}\). Also, \(\overline{TU}\cong\overline{WV}\) and \(\overline{UV}\cong\overline{WT}\), which satisfies the properties of a rectangle (opposite sides equal and all angles \(90^{\circ}\)).

Step3: Check for square properties

If \(\overline{TU}\cong\overline{WV}\cong\overline{UV}\cong\overline{WT}\) (from \(\overline{TU}\cong\overline{WV}\), \(\overline{UV}\cong\overline{WT}\) and if all - sides are equal in length) and all angles are \(90^{\circ}\), it also satisfies the properties of a square (a special case of a rectangle with all sides equal).

A parallelogram has opposite sides equal and parallel but does not necessarily have all angles equal to \(90^{\circ}\). A rhombus has all sides equal but not necessarily all angles equal to \(90^{\circ}\). A trapezoid has only one pair of parallel sides (not satisfied here as we have a more regular quadrilateral).

Answer:

• Quadrilateral
• Rectangle
• Square