Decide whether each of this statements is always, sometimes, or never ever true. ÂIf the is sometimes true, draw and also describe a figure for i beg your pardon the explain is true and another number for which the declare is not true.

You are watching: A rectangle is a rhombus true or false

## IM Commentary

The purpose of this task is to have students reason around different kinds of shapes based upon their specifying attributes and also to understand the relationship between different category of shapes that re-superstructure some defining attributes. In cases when the list of defining characteristics for the very first shape is a subset of the defining features of the second shape, climate the statements will always be true.ÂIn situations when the list of defining qualities for the second shape is a subset of the defining attributes of the very first shape, then the explanation will occasionally be true.

When this task is supplied in instruction, teachers must be prioritizing the conventional for Mathematical exercise 6: attend to Precision. Students should base their reasoning by referring to side 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 actually 4 right angles. ÂIt is no true when a rhombus does not have any kind of right angles.

Here is an example when a rhombus is a square:

Here is an instance when a rhombus is *not* a square:

2. A triangle is a parallelogram.

This is *never* true. ÂA triangle is a three-sided figure. ÂA parallelogram is a four-sided figure with 2 sets that parallel sides.

3. A square is a parallelogram.

This is *always* true. ÂSquares space quadrilaterals through 4 congruent sides and 4 ideal angles, and also they also have two sets of parallel sides. Parallelograms space quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals v two sets of parallel sides, then every squares are parallelograms.

4. AÂsquare is a rhombus

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

5. A parallel is a rectangle.

This is *sometimes* true. ÂIt is true when the parallelogram has 4 right angles. ÂIt is no true once a parallelogram has no ideal angles.

Here is an instance when a parallelogram is a rectangle:

Here is an example 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, for this reason they must always be quadrilaterals.