Is A Parallelogram A Square

Always, Sometimes, Never

Alignments to Content Standards: five.Chiliad.B.3

Task

Determine whether each of these statements is ever, sometimes, or never truthful. If it is sometimes true, draw and describe a effigy for which the statement is truthful and another effigy for which the statement is not truthful.

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

IM Commentary

The purpose of this task is to have students reason virtually different kinds of shapes based on their defining attributes and to understand the human relationship between different categories of shapes that share some defining attributes. In cases when the listing of defining attributes for the start shape is a subset of the defining attributes of the second shape, then the statements will always be true. In cases when the list of defining attributes for the second shape is a subset of the defining attributes of the outset shape, and then the statements volition sometimes exist true.

When this chore is used in instruction, teachers should exist prioritizing the Standard for Mathematical Practice 6: Attend to Precision. Students should base their reasoning past referring to side length, side relationships, and angle measures.

Solution

1. A rhomb is a square.

This is sometimes true. Information technology is true when a rhomb has 4 right angles. Information technology is not true when a rhombus does not have any correct angles.

Here is an example 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. A triangle is a three-sided figure. A parallelogram is a four-sided figure with two sets of parallel sides.

three. A square is a parallelogram.

This is always true. Squares are quadrilaterals with 4 coinciding sides and iv right angles, and they also accept two sets of parallel sides. Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, and then all squares are parallelograms.

4. A square is a rhombus

This is ever true. Squares are quadrilaterals with 4 congruent sides. Since rhombuses are quadrilaterals with 4 congruent sides, squares are by definition also rhombuses.

5. A parallelogram is a rectangle.

This is sometimes true. Information technology is true when the parallelogram has four right angles. It is not truthful when a parallelogram has no right angles.

Here is an case when a parallelogram is a rectangle:

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

six. A trapezoid is a quadrilateral.

This is e'er true. Trapezoids must have 4 sides, then they must always exist quadrilaterals.

Is A Parallelogram A Square,

Source: http://tasks.illustrativemathematics.org/content-standards/5/G/B/3/tasks/1941#:~:text=A%20square%20is%20a%20parallelogram.,two%20sets%20of%20parallel%20sides.

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