Decide whether every of these statements is always, sometimes, or never ever true. ÂIf the is periodically true, draw and describe a number for which the explain is true and also another number for i m sorry the declare is no true.

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

## IM Commentary

The objective of this task is to have actually students reason around different kinds of shapes based upon their specifying attributes and to recognize the relationship between different categories of forms that re-publishing some specifying attributes. In instances when the list of defining qualities for the first shape is a subset the the defining features of the second shape, climate the statements will always be true.ÂIn situations when the list of defining characteristics for the second shape is a subset that the defining qualities of the first shape, then the explanation will occasionally be true.

When this job is supplied in instruction, teachers must be prioritizing the traditional for Mathematical exercise 6: address Precision. Students have to base their thinking by referring to next length, next relationships, and also angle measures.

## Solution

1. A rhombus is a square.

This is *sometimes* true. ÂIt is true when a rhombus has actually 4 right angles. ÂIt is not true when a rhombus does not have any type of right angles.

Here is an instance when a rhombus is a square:

Here is an example 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 two sets that parallel sides.

3. A square is a parallelogram.

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

4. AÂsquare is a rhombus

This is *always*Âtrue. ÂSquares space quadrilaterals through 4 congruent sides. ÂSince rhombuses room quadrilaterals v 4 congruent sides, squares space 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 right 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:

Here is an example when a parallelogram 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 always be quadrilaterals.