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

You are watching: Is a parallelogram always a rectangle

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

IM Commentary

The objective of this job is to have students reason about different kinds of shapes based on their defining attributes and also to understand the relationship in between different categories of forms that re-publishing some specifying attributes. In situations when the perform of defining qualities for the very first shape is a subset the the defining attributes of the second shape, climate the declaration will always be true.ÂIn cases when the perform of defining characteristics for the second shape is a subset that the defining characteristics of the an initial shape, climate the explanation will periodically be true.

When this job is provided in instruction, teachers must be prioritizing the conventional for Mathematical practice 6: deal with Precision. Students need to base their reasoning by introduce to next length, side relationships, and angle measures.


Solution

1. A rhombus is a square.

This is sometimes true. ÂIt is true once a rhombus has 4 right angles. ÂIt is no true once a rhombus does no have any type of right angles.

Here is an instance when a rhombus is a square:

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Here is an instance 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 of parallel sides.

3. A square is a parallelogram.

This is always true. ÂSquares room quadrilaterals with 4 congruent sides and 4 appropriate angles, and also they also have two sets of parallel sides. Parallelograms are quadrilaterals through two set of parallel sides. Since squares should be quadrilaterals through two set of parallel sides, then all squares are parallelograms.

4. AÂsquare is a rhombus

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

5. A parallelogram is a rectangle.

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

Here is an example when a parallelogram is a rectangle:

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

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6. A trapezoid is a quadrilateral.

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