Decide whether each of these statements is always, sometimes, or never true. ÂIf that is occasionally true, draw and also describe a number for which the declare is true and another number for i m sorry the declare is not true.

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A rhombus is a square A triangle is a parallelogram A square is a parallelogram 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 around different type of shapes based on their specifying attributes and also to understand the relationship in between different category of shapes that re-publishing some specifying attributes. In cases when the list of defining qualities for the first shape is a subset of the defining qualities of the 2nd shape, climate the statements will constantly be true.ÂIn situations when the perform of defining characteristics for the second shape is a subset of the defining attributes of the first shape, then the declaration will occasionally be true.

When this job is provided in instruction, teachers must be prioritizing the traditional for Mathematical exercise 6: attend to Precision. Students should 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 when a rhombus has 4 ideal angles. ÂIt is not true once a rhombus does no have any right angles.

Here is an example when a rhombus is a square:

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Here is an example 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 parallelogram is a four-sided figure with two sets that parallel sides.

3. A square is a parallelogram.

This is always true. ÂSquares space quadrilaterals with 4 congruent sides and 4 appropriate angles, and they likewise have two sets of parallel sides. Parallelograms room quadrilaterals with two set of parallel sides. Since squares need to be quadrilaterals with two to adjust of parallel sides, then all squares space parallelograms.

4. AÂsquare is a rhombus

This is alwaysÂtrue. ÂSquares are quadrilaterals with 4 congruent sides. ÂSince rhombuses are quadrilaterals through 4 congruent sides, squares space by definition also rhombuses. Â

5. A parallelogram is a rectangle.

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

Here is an instance when a parallel is a rectangle:

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Here is an instance when a parallel 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 actually 4 sides, so they must constantly be quadrilaterals.