Question

if a quadnlateral has exactly 2 lines of symmetry, and both are angle bisectors, then which statement would be true? the figure must be an isosceles trapezoid because it has 2 congruent base angles the figure must be a rectangle because all rectangles have exactly 2 lines of symmetry the figure could be a rhombus because the 2 lines of symmetry bisect the angles the figure could be a square because the diagonals of a square bisect the right angles

Explanation:

Step1: Analyze isosceles trapezoid

An isosceles trapezoid has only 1 line of symmetry (the line that is the perpendicular bisector of the bases). So the first option is wrong.

Step2: Analyze rectangle

A rectangle has 2 lines of symmetry (the lines joining the mid - points of opposite sides), but these lines are not angle bisectors (except when it is a square). So the second option is wrong.

Step3: Analyze rhombus

A rhombus has 2 lines of symmetry (its diagonals). The diagonals of a rhombus bisect the angles. So the third option is correct.

Step4: Analyze square

A square has 4 lines of symmetry (2 diagonals and 2 lines joining the mid - points of opposite sides). So the fourth option is wrong.

Answer:

C. The figure could be a rhombus because the 2 lines of symmetry bisect the angles