Decide whether each of these statements is always, sometimes, or never true. If it is occasionally true, draw and also define a figure for which the statement is true and also one more figure for which the statement is not true.

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

IM Commentary

The function of this job is to have students reason about various kinds of forms based upon their specifying attributes and also to understand also the relationship between different categories of shapes that share some specifying attributes. In situations when the list of specifying features for the first shape is a subset of the defining features of the second shape, then the statements will certainly constantly be true. In situations as soon as the list of specifying features for the second shape is a subset of the specifying attributes of the initially form, then the statements will certainly sometimes be true.

When this job is provided in instruction, teachers should be prioritizing the Standard for Mathematical Practice 6: Attend to Precision. Students must base their reasoning by referring to side size, side relationships, and also angle steps.


Solution

1. A rhombus is a square.

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

Here is an example as soon as a rhombus is a square:

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Here is an instance once a rhombus is not a square:

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2. A triangle is a parallelogram.

This is never true. A triangle is a three-sided figure. A parallelogram is a four-sided number through two sets of parallel sides.

3. A square is a parallelogram.

This is always true. Squares are quadrilaterals via 4 congruent sides and 4 best angles, and they additionally have 2 sets of parallel sides. Parallelograms are quadrilaterals through 2 sets of parallel sides. Due to the fact that squares must be quadrilaterals through 2 sets of parallel sides, then all squares are parallelograms.

4. A square is a rhombus

This is always true. Squares are quadrilaterals via 4 congruent sides. Due to the fact that rhomboffers are quadrilaterals through 4 congruent sides, squares are by meaning additionally rhomboffers.

5. A parallelogram is a rectangle.

This is sometimes true. It is true once the parallelogram has 4 best angles. It is not true when a parallelogram has actually no right angles.

Here is an example when a parallelogram is a rectangle:

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Here is an example once a parallelogram is not a rectangle:

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6. A trapezoid is a quadrilateral.

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This is always true. Trapezoids must have 4 sides, so they have to always be quadrilaterals.