Question

!50 POINTS! (3 SIMPLE GEOMETRY QUESTIONS)

QUESTIONS BELOW
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Answer 1

1) Rhombus

2) Rectangle

3) Square

Explanation:

A quadrilateral is a polygon with four sides and four vertices.

There are several different types of quadrilaterals, each with its own unique characteristics. The main types of quadrilaterals include:

• Rectangle, Square, Parallelogram, Rhombus, Trapezoid, Kite.

To identify the different types of quadrilaterals, we need to examine their specific properties.

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Question 1

From the given answer options of rhombus, parallelogram, square and rectangle, a rectangle is the only quadrilateral that cannot have all sides of equal length (as it would then be called a square).

Any parallelogram or rectangle in which the diagonals are perpendicular bisectors of each other would be called a square. So we can discount the quadrilateral being a parallelogram or a rectangle.

The diagonals in a square are congruent. Therefore, as the diagonals in John's quadrilateral are not congruent, John drew is a Rhombus.

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Question 2

From the given answer options of parallelogram, rectangle, square and rhombus, a square and rectangle are the only quadrilaterals where all four angles are right angles. (If a rhombus or a parallelogram have interior right angles, they would be called a square or a rectangle).

The diagonals of a square and a rectangle are congruent, as are their opposite sides.

Since all sides of a square are of equal length, and we have only been told that opposite sides are congruent, John drew a rectangle.

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Question 3

From the given answer options of parallelogram, square, rectangle and rhombus, a rectangle is the only quadrilateral that cannot have all sides of equal length (as it would then be called a square).

Any parallelogram or rectangle in which the diagonals are perpendicular bisectors of each other would be called a square. So we can discount the quadrilateral being a parallelogram or a rectangle.

If the interior angles of a quadrilateral were right angles, it would be called a square or a rectangle. As we have already discounted the quadrilateral being a rectangle, John drew a square.