SOLUTION: Consider the statement, “If a parallelogram is a square, then it is a rhombus.” A) Decide whether it is sometimes/always/never true. B) Write the converse of the statement.

Algebra ->  Parallelograms -> SOLUTION: Consider the statement, “If a parallelogram is a square, then it is a rhombus.” A) Decide whether it is sometimes/always/never true. B) Write the converse of the statement.      Log On


   

Question 1178664: Consider the statement, “If a parallelogram is a square, then it is a rhombus.”
A) Decide whether it is sometimes/always/never true.
B) Write the converse of the statement.
C) Decide whether the converse is sometimes/always/never true.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Consider the statement, “If a parallelogram is a square, then it is a rhombus.”
A) Decide whether it is sometimes/always/never true.
If a parallelogram has perpendicular diagonals, you know it is a rhombus
so, always true
B) Write the converse of the statement.
Converse:
if a parallelogram is a rhombus, then it is a square

C) Decide whether the converse is sometimes/always/never true.
a) sometimes+
(A rhombus is a quadrilateral with all sides equal in length. A square is a quadrilateral with all sides equal in length and all interior angles right angles. Thus a rhombus is not a square unless the angles are all right angles.)