3. If x = 4, x2 = 16
This statement can be written as x = 4 → x2 = 16. It is true because if x is 4, then x2 is 16 by the definition of squaring.
The converse of this statement is x2 = 16 → x = 4. It is false because there are two possible values of x that satisfy x2 = 16, namely 4 and -4. A counterexample is x = -4.
4. If one angle of a quadrilateral is a right angle, then the quadrilateral is a rectangle.
This statement can be written as one angle of a quadrilateral is a right angle → the quadrilateral is a rectangle. It is false because there are quadrilaterals with one right angle that are not rectangles, such as trapezoids or kites. A counterexample is a trapezoid with one right angle.
The converse of this statement is the quadrilateral is a rectangle → one angle of a quadrilateral is a right angle. It is true because all rectangles have four right angles by definition.
5. If a triangle is equilateral, then it has three equal angles.
This statement can be written as a triangle is equilateral → it has three equal angles. It is true because all equilateral triangles have three equal angles of 60 degrees by definition.
The converse of this statement is it has three equal angles → a triangle is equilateral. It is true because if a triangle has three equal angles, then they must be 60 degrees each, and therefore the triangle must be equilateral by definition.