Decide whether each of this statements is always, sometimes, or never true. If it is occasionally true, draw and describe a figure for i m sorry the declare is true and another figure for i m sorry the declare is not true.

You are watching: Is a parallelogram always a square

## IM Commentary

The objective of this job is to have actually students reason about different type of shapes based on their defining attributes and also to recognize the relationship in between different category of forms that re-superstructure some defining attributes. In situations when the perform of defining qualities for the an initial shape is a subset of the defining features of the 2nd shape, climate the explanation will always be true. In instances when the perform of defining features for the 2nd shape is a subset the the defining features of the very first shape, then the statements will occasionally be true.

When this job is used in instruction, teachers have to be prioritizing the conventional for Mathematical practice 6: attend to Precision. Students need to 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. That is true when a rhombus has 4 best angles. The is not true once a rhombus does not have any kind of right angles.

Here is an instance 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 room quadrilaterals v 4 congruent sides and 4 right angles, and also they additionally have two sets that parallel sides. Parallelograms are quadrilaterals with two set of parallel sides. Since squares need to be quadrilaterals through two to adjust of parallel sides, then all squares are parallelograms.

4. A square is a rhombus

This is *always* true. Squares space quadrilaterals through 4 congruent sides. Because rhombuses space quadrilaterals through 4 congruent sides, squares room by definition also rhombuses.

5. A parallel is a rectangle.

This is *sometimes* true. It is true when the parallelogram has 4 best angles. It is no true when a parallelogram has no appropriate angles.

Here is an example when a parallelogram 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. Trapezoids must have actually 4 sides, so they must always be quadrilaterals.