Which statements are true?

If all angles of a quadrilateral are right angles, then the quadrilateral must be a square.

Two shapes are similar if and only if their corresponding angles are equal.

All quadrilaterals have four sides, and the sum of all angles in a quadrilateral is 180°.

If the diagonals of a quadrilateral are perpendicular bisectors, then the quadrilateral must be a rhombus.

There are three vertices in a triangle, or there are four sides in a pentagon.

Any two triangles are either similar or congruent.

In a rhombus, the diagonals bisect at perpendicular angles to form 4 triangles.Because the diagonals bisect at right angles, then it is possible to prove that the four small formed triangles are similar using the SAS theorem: two triangles are equal if two sides are equal and the angles between the two sides are equal.In your case, the sides are that on the base and that forming a height of the triangles with both having angle 90° between the sides.So you see if these the two are congruent, the hypotenuse of these triangles are congruent, making this quadrilateral a rhombus.

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Keywords : quadrilateral, rhombus, perpendicular bisector, angles

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