Consider parallelogram WXYZ below. Y Z Note that WXYZ has vertices W (5, 2), X (1, -5), Y (-6, -1), and Z (-2, 6). Answer the following to determine if the parallelogram is a rectangle, rhombus, square, or none of these.

Question

15-10-2023
Mathematics

High School

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Consider parallelogram WXYZ below. Y Z Note that WXYZ has vertices W (5, 2), X (1, -5), Y (-6, -1), and Z (-2, 6). Answer the following to determine if the parallelogram is a rectangle, rhombus, square, or none of these.

Answer :

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Final answer:

To determine the classification of parallelogram WXYZ, we need to check its properties as a rectangle, rhombus, and square.

Explanation:

The given vertices of parallelogram WXYZ are W(5, 2), X(1, -5), Y(-6, -1), and Z(-2, 6). To determine if the parallelogram is a rectangle, rhombus, square, or none of these, we need to check the properties of these quadrilaterals.

Rectangle: A parallelogram is a rectangle if all its angles are 90 degrees. We can find the slopes of opposite sides of the parallelogram and check if the product of the slopes is -1, which indicates perpendicularity. If the product is -1, the parallelogram is a rectangle.

Rhombus: A parallelogram is a rhombus if all its sides are congruent. We can find the lengths of opposite sides of the parallelogram and check if they are equal. If the lengths are equal, the parallelogram is a rhombus.

Square: A parallelogram is a square if it is both a rectangle and a rhombus. If the parallelogram satisfies both the conditions of being a rectangle and a rhombus, it is a square.

By calculating the slopes and lengths of sides of parallelogram WXYZ, we can determine its classification.

Consider parallelogram WXYZ below. Y Z Note that WXYZ has vertices W (5, 2), X (1, -5), Y (-6, -1), and Z (-2, 6). Answer the following to determine if the parallelogram is a rectangle, rhombus, square, or none of these.​

Answer :

Final answer:

Explanation:

Other Questions

Consider parallelogram WXYZ below. Y Z Note that WXYZ has vertices W (5, 2), X (1, -5), Y (-6, -1), and Z (-2, 6). Answer the following to determine if the parallelogram is a rectangle, rhombus, square, or none of these.