To evaluate the given statements, we start by recognizing that a quadrilateral with exactly 2 lines of symmetry that are both angle bisectors typically has a certain shape.
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The figure must be an isosceles trapezoid because it has 2 congruent base angles.
- This statement is true in the sense that an isosceles trapezoid has a line of symmetry along the vertical line that bisects the bases and the angles at the top and bottom. It can have 2 lines of symmetry if we consider the angle bisectors as the lines that bisect the top and bottom angles, leading to the conclusion that it could be an isosceles trapezoid; however, it is not definitive that this is the only shape.
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The figure must be a rectangle because all rectangles have exactly 2 lines of symmetry.
- This statement is false; while rectangles do have lines of symmetry, they also have 4 lines of symmetry (two vertical and two horizontal). Therefore, a rectangle does not fit the criteria of having exactly 2 lines of symmetry.
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The figure could be a rhombus because the 2 lines of symmetry bisect the angles.
- A rhombus does have 2 lines of symmetry that are the diagonals, and they indeed bisect the angles. Therefore, a rhombus fits this description.
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The figure could be a square because the diagonals of a square bisect the right angles.
- A square is a specific type of rhombus, and it does have 4 lines of symmetry (two diagonals and two midlines). Thus, while this statement is true about a square having diagonals that bisect angles, it does not fit the criteria of having exactly 2 lines of symmetry.
From our evaluations, the best fitting statement that satisfies the criteria of having exactly 2 lines of symmetry (which are angle bisectors) is:
The figure could be a rhombus because the 2 lines of symmetry bisect the angles.
Thus, the true statement is that the figure could be a rhombus.
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