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Classify the Following Statements as True or False

Question 10

Matching

Classify the following statements as true or false. If an item is false, sketch a counterexample.

Premises:

Responses:

Any fact that is true for every parallelogram is also true for every square.

False

The diagonals of a rhombus are congruent.

True

Every rhombus is a kite.

The opposite angles of a parallelogram are congruent.

Every equilateral triangle is an isosceles triangle.

Any fact that is true for every rectangle is also true for every quadrilateral.

Every rectangle is a square.

The diagonals of a rectangle bisect each other.

Every square is a quadrilateral.

Every trapezoid is a parallelogram.

Premises:

Any fact that is true for every parallelogram is also true for every square.

The diagonals of a rhombus are congruent.

Every rhombus is a kite.

The opposite angles of a parallelogram are congruent.

Every equilateral triangle is an isosceles triangle.

Any fact that is true for every rectangle is also true for every quadrilateral.

Every rectangle is a square.

The diagonals of a rectangle bisect each other.

Every square is a quadrilateral.

Every trapezoid is a parallelogram.

Responses:

False

True

Correct Answer:

Premises:

Responses:

Any fact that is true for every parallelogram is also true for every square.

The diagonals of a rhombus are congruent.

Every rhombus is a kite.

The opposite angles of a parallelogram are congruent.

Every equilateral triangle is an isosceles triangle.

Any fact that is true for every rectangle is also true for every quadrilateral.

Every rectangle is a square.

The diagonals of a rectangle bisect each other.

Every square is a quadrilateral.

Every trapezoid is a parallelogram.