Decide whether every of these statements is always, sometimes, or never true. ÂIf that is sometimes true, draw and describe a number for which the declare is true and also another number for which the declare is not true.

You are watching: A square is always a rhombus true or false

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

IM Commentary

The purpose of this task is to have actually students reason about different type of shapes based upon their defining attributes and also to understand the relationship between different categories of forms that share some specifying attributes. In cases when the list of defining features for the an initial shape is a subset the the defining qualities of the second shape, climate the explanation will constantly be true.ÂIn cases when the list of defining features for the second shape is a subset that the defining attributes of the an initial shape, climate the statements will sometimes be true.

When this task is supplied in instruction, teachers need to be prioritizing the traditional for Mathematical exercise 6: deal with Precision. Students must base their thinking by referring to side length, next relationships, and angle measures.


Solution

1. A rhombus is a square.

This is sometimes true. ÂIt is true when a rhombus has 4 right angles. ÂIt is not true as soon as 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. ÂA triangle is a three-sided figure. ÂA parallel is a four-sided number with two sets that parallel sides.

3. A square is a parallelogram.

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

4. AÂsquare is a rhombus

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

5. A parallel is a rectangle.

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

Here is an instance when a parallel is a rectangle:

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

*

6. A trapezoid is a quadrilateral.

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This is always true. ÂTrapezoids must have actually 4 sides, therefore they must constantly be quadrilaterals.