Decide whether every of these statements is always, sometimes, or never ever true. If the is periodically true, draw and also describe a number for which the declare is true and another figure for i m sorry the explain is not true.

You are watching: Are all squares parallelograms true or false

## 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 understand the relationship in between different categories of forms that re-publishing some defining attributes. In instances when the list of defining qualities for the very first shape is a subset the the defining qualities of the 2nd shape, then the explanation will always be true. In cases when the perform of defining characteristics for the second shape is a subset the the defining attributes of the an initial shape, climate the statements will periodically be true.

When this job is offered in instruction, teachers should be prioritizing the typical for Mathematical practice 6: resolve Precision. Students must base their thinking by referring to next length, next relationships, and angle measures.

## Solution

1. A rhombus is a square.

This is *sometimes* true. That is true once a rhombus has 4 appropriate angles. It is no true as soon as a rhombus does not have any type of right angles.

Here is an instance when a rhombus is a square:

Here is an example 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 parallel is a four-sided figure with two sets the parallel sides.

3. A square is a parallelogram.

This is *always* true. Squares are quadrilaterals with 4 congruent sides and 4 ideal angles, and also they additionally have 2 sets that parallel sides. Parallelograms space quadrilaterals v two to adjust of parallel sides. Due to the fact that squares should be quadrilaterals with two set of parallel sides, then all squares space parallelograms.

4. A square is a rhombus

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

5. A parallelogram is a rectangle.

This is *sometimes* true. It is true as soon as the parallelogram has actually 4 right angles. That is not true once a parallelogram has 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 4 sides, therefore they must constantly be quadrilaterals.