Decide whether every of these statements is always, sometimes, or never ever true. ÂIf that is periodically true, draw and also describe a number for i beg your pardon the statement is true and another number for which the declare is not true.

You are watching: A square is a rectangle. always sometimes never

A rhombus is a square A triangle is a parallelogram A square is a parallel AÂsquare is a rhombus A parallelogram is a rectangle A trapezoid is a quadrilateral

IM Commentary

The function of this job is to have students reason around different kinds of shapes based on their specifying attributes and also to know the relationship between different category of forms that share some defining attributes. In instances when the perform of defining qualities for the first shape is a subset of the defining features of the 2nd shape, climate the explanation will constantly be true.ÂIn cases when the list of defining characteristics for the second shape is a subset the the defining attributes of the an initial shape, climate the declaration will sometimes be true.

When this task is used in instruction, teachers have to be prioritizing the typical for Mathematical practice 6: attend to Precision. Students should base their reasoning by introduce to side length, side relationships, and also angle measures.


Solution

1. A rhombus is a square.

This is sometimes true. ÂIt is true as soon as a rhombus has 4 ideal angles. ÂIt is not true once a rhombus does no have any type of right angles.

Here is an example when a rhombus is a square:

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Here is an example when a rhombus is not a square:

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2. A triangle is a parallelogram.

This is never true. ÂA triangle is a three-sided figure. ÂA parallel is a four-sided figure with two sets the parallel sides.

3. A square is a parallelogram.

This is always true. ÂSquares room quadrilaterals v 4 congruent sides and also 4 ideal angles, and also they additionally have two sets the parallel sides. Parallelograms are quadrilaterals v two set of parallel sides. Since squares have to be quadrilaterals through two sets of parallel sides, then every squares space parallelograms.

4. AÂsquare is a rhombus

This is alwaysÂtrue. ÂSquares are quadrilaterals through 4 congruent sides. ÂSince rhombuses are quadrilaterals through 4 congruent sides, squares space by meaning also rhombuses. Â

5. A parallelogram is a rectangle.

This is sometimes true. ÂIt is true as soon as the parallelogram has 4 ideal angles. ÂIt is not true once a parallelogram has actually no appropriate angles.

Here is an instance when a parallel is a rectangle:

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Here is an example when a parallelogram is not a rectangle:

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6. A trapezoid is a quadrilateral.

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This is always true. ÂTrapezoids must have 4 sides, therefore they must constantly be quadrilaterals.