Question

if a quadrilateral 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 1 line of symmetry. So it cannot be the answer as we need a quadrilateral with 2 lines of symmetry.

Step2: Analyze rectangle

A rectangle has 2 lines of symmetry, but its lines of symmetry are not angle - bisectors in general (only in the case of a square which is a special rectangle). So this is incorrect.

Step3: Analyze rhombus

A rhombus has 2 lines of symmetry and these lines of symmetry are the angle - bisectors of the angles of the rhombus. This satisfies the given condition.

Step4: Analyze square

A square has 4 lines of symmetry, not 2. So it does not meet the requirement of having exactly 2 lines of symmetry.

Answer:

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