Decide whether each of this statements is always, sometimes, or never true. If that is sometimes true, draw and also describe a figure for i beg your pardon the statement is true and also another figure for which the explain is no true.

You are watching: Are all squares parallelograms true or false

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

IM Commentary

The objective of this task is to have actually students reason around different kinds of shapes based on their defining attributes and to recognize the relationship between different categories of shapes that re-publishing some specifying attributes. In instances when the list of defining attributes for the first shape is a subset of the defining features of the 2nd shape, climate the explanation will constantly be true. In situations when the perform of defining characteristics for the 2nd shape is a subset that the defining attributes of the very first shape, climate the declaration will sometimes be true.

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


Solution

1. A rhombus is a square.

This is sometimes true. The is true when a rhombus has actually 4 appropriate angles. It is not true when a rhombus does not have any 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. A triangle is a three-sided figure. A parallel is a four-sided figure with two sets of parallel sides.

3. A square is a parallelogram.

This is always true. Squares space quadrilaterals with 4 congruent sides and also 4 best angles, and also they likewise have two sets the parallel sides. Parallelograms space quadrilaterals through two sets of parallel sides. Because squares need to be quadrilaterals v two sets of parallel sides, then all squares space parallelograms.

4. A square is a rhombus

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

5. A parallel is a rectangle.

This is sometimes true. That is true once the parallelogram has actually 4 right angles. It is not true when a parallelogram has no right angles.

Here is an example when a parallel is a rectangle:

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

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6. A trapezoid is a quadrilateral.

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