Decide whether each of this statements is always, sometimes, or never ever true. ÂIf that is occasionally true, draw and also describe a figure for i m sorry the explain is true and another number for which the explain is no 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 parallel AÂsquare is a rhombus A parallelogram is a rectangle A trapezoid is a quadrilateral

IM Commentary

The objective of this job is to have students reason around different type of shapes based upon their defining attributes and to understand the relationship between different category of shapes that re-superstructure some specifying attributes. In instances when the list of defining features for the first shape is a subset that the defining qualities of the 2nd shape, then the statements will constantly be true.ÂIn situations when the list of defining qualities for the 2nd shape is a subset of the defining attributes of the an initial shape, climate the declaration will occasionally be true.

When this job is used in instruction, teachers have to be prioritizing the conventional for Mathematical practice 6: address Precision. Students must base their thinking by introduce to next length, side relationships, and also angle measures.


Solution

1. A rhombus is a square.

This is sometimes true. ÂIt is true as soon as a rhombus has actually 4 appropriate angles. ÂIt 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 instance when a rhombus is not a square:

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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 that parallel sides.

3. A square is a parallelogram.

This is always true. ÂSquares room quadrilaterals with 4 congruent sides and 4 best angles, and also they additionally have two sets of parallel sides. Parallelograms room quadrilaterals through two set of parallel sides. Because squares must be quadrilaterals with two set of parallel sides, then every squares space parallelograms.

4. AÂsquare is a rhombus

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

5. A parallelogram is a rectangle.

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

Here is an instance 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. ÂTrapezoids must have 4 sides, for this reason they must always be quadrilaterals.