Decide whether every of this statements is always, sometimes, or never true. ÂIf it is periodically true, draw and also describe a number for i beg your pardon the declare is true and also another figure for i m sorry the declare is not true.

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

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

IM Commentary

The purpose of this task is to have students reason about different kinds of shapes based on their specifying attributes and also to understand the relationship between different categories of forms that share some specifying attributes. In instances when the perform of defining qualities for the an initial shape is a subset that the defining qualities of the second shape, climate the declaration will always be true.ÂIn instances when the perform of defining features for the 2nd shape is a subset that the defining qualities of the first shape, then the declaration will periodically be true.

When this job is supplied in instruction, teachers have to be prioritizing the standard for Mathematical practice 6: attend to Precision. Students must base their thinking by introduce to next length, next 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 4 best angles. ÂIt is not true as soon as a rhombus does not have any type of right angles.

Here is an instance 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. ÂA triangle is a three-sided figure. ÂA parallel is a four-sided number with two sets the parallel sides.

3. A square is a parallelogram.

This is always true. ÂSquares are quadrilaterals v 4 congruent sides and also 4 appropriate angles, and also they also have two sets the parallel sides. Parallelograms room quadrilaterals v two set of parallel sides. Due to the fact that squares should be quadrilaterals v two sets of parallel sides, then all squares room parallelograms.

4. AÂsquare is a rhombus

This is alwaysÂtrue. ÂSquares room quadrilaterals through 4 congruent sides. ÂSince rhombuses are quadrilaterals with 4 congruent sides, squares room by definition also rhombuses. Â

5. A parallelogram is a rectangle.

This is sometimes true. ÂIt is true as soon as the parallelogram has 4 ideal angles. ÂIt is not true once a parallelogram has no best angles.

Here is an example when a parallelogram is a rectangle:

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