Decide whether each of this statements is always, sometimes, or never ever true. If it is sometimes true, draw and also describe a number for i beg your pardon the explain is true and another number for which the declare is not true.

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

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

## IM Commentary

The objective of this task is to have students reason about different type of shapes based upon their defining attributes and to recognize the relationship in between different categories of forms that re-superstructure some specifying attributes. In cases when the list of defining characteristics for the very first shape is a subset the the defining qualities of the second shape, then the statements will always be true. In cases when the list of defining features for the second shape is a subset that the defining attributes of the first shape, climate the statements will occasionally be true.

When this task is provided in instruction, teachers need to be prioritizing the standard for Mathematical practice 6: deal with Precision. Students have to base their reasoning by referring to next length, next relationships, and angle measures.

## Solution

1. A rhombus is a square.

This is sometimes true. It is true as soon as a rhombus has 4 ideal angles. That is no true once 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. A triangle is a three-sided figure. A parallelogram is a four-sided number with 2 sets the parallel sides.

3. A square is a parallelogram.

This is always true. Squares space quadrilaterals v 4 congruent sides and 4 appropriate angles, and they likewise have two sets of parallel sides. Parallelograms are quadrilaterals v two to adjust of parallel sides. Due to the fact that squares need to be quadrilaterals v two to adjust of parallel sides, then every squares room parallelograms.

4. A square is a rhombus

This is always true. Squares are quadrilaterals through 4 congruent sides. Since rhombuses room quadrilaterals v 4 congruent sides, squares space by an interpretation also rhombuses.

5. A parallelogram is a rectangle.

This is sometimes true. That is true once the parallelogram has actually 4 best angles. That is no true as soon as a parallelogram has actually no right angles.

Here is an example when a parallelogram is a rectangle:

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

6. A trapezoid is a quadrilateral.

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This is always true. Trapezoids must have actually 4 sides, for this reason they must always be quadrilaterals.