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

You are watching: A rhombus is a square always sometimes never

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

## IM Commentary

The function of this task is to have students reason about different kinds of shapes based upon their defining attributes and to recognize the relationship between different category of shapes that re-superstructure some specifying attributes. In instances when the list of defining features for the an initial shape is a subset the the defining qualities of the second shape, then the explanation will always be true.ÂIn instances when the list of defining qualities for the 2nd shape is a subset of the defining attributes of the an initial shape, then the statements will sometimes be true.

When this task is offered in instruction, teachers have to be prioritizing the typical for Mathematical exercise 6: resolve Precision. Students should base their thinking by referring to side length, side relationships, and also angle measures.

## Solution

1. A rhombus is a square.

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

Here is an example when a rhombus is a square:

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

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 of parallel sides.

3. A square is a parallelogram.

This is always true. ÂSquares space quadrilaterals with 4 congruent sides and also 4 appropriate angles, and also they also have 2 sets of parallel sides. Parallelograms are quadrilaterals through two set of parallel sides. Since squares must be quadrilaterals through two to adjust of parallel sides, then every squares are parallelograms.

4. AÂsquare is a rhombus

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

5. A parallel is a rectangle.

This is sometimes true. ÂIt is true when the parallelogram has 4 best angles. ÂIt is not true when a parallelogram has actually no best angles.

Here is an example when a parallel is a rectangle:

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

6. A trapezoid is a quadrilateral.

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