If a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, then which statement would be true?
Answer
A
The figure must be an isosceles trapezoid because it has 2 congruent base angles.
B
The figure must be a rectangle because all rectangles have exactly 2 lines of symmetry.
C
The figure could be a square because the diagonals of a square bisect the right angles.
D
The figure could be a rhombus because the 2 lines of symmetry bisect the angles.
Explanation
A non-square rhombus has exactly two lines of symmetry: its diagonals. Each diagonal bisects the angles at the vertices it connects, so both symmetry lines are angle bisectors. A square also has diagonal angle-bisector symmetry, but it has four lines of symmetry, not exactly two.
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