Decide whether each of these statements is always, sometimes, or never ever true. ÂIf it is periodically true, draw and 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 trapezoid is never a parallelogram

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

## IM Commentary

The purpose of this job is to have students reason about different type of shapes based upon their specifying attributes and to recognize the relationship between different categories of shapes that re-publishing some defining attributes. In situations when the perform of defining attributes for the very first shape is a subset of the defining features of the 2nd shape, climate the statements will always be true.ÂIn cases when the list of defining characteristics for the second shape is a subset of the defining features of the very first shape, climate the statements will periodically be true.

When this job is used in instruction, teachers have to be prioritizing the conventional for Mathematical practice 6: resolve Precision. Students should base their reasoning by introduce 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 4 ideal angles. ÂIt is not true when a rhombus does no have any type 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 parallel is a four-sided number with 2 sets of parallel sides.

3. A square is a parallelogram.

This is always true. ÂSquares space quadrilaterals through 4 congruent sides and also 4 appropriate angles, and they additionally have two sets of parallel sides. Parallelograms space quadrilaterals through two to adjust of parallel sides. Due to the fact that squares have to be quadrilaterals through two sets of parallel sides, then every squares space parallelograms.

4. AÂsquare is a rhombus

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

5. A parallel is a rectangle.

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

Here is an example when a parallel is a rectangle: Here is an instance 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, so they must constantly be quadrilaterals.