Question

Which of the following statements is false for a rectangle?
(a) All rectangles are squares.
(b) Its diagonals are perpendicular.
(c) Its diagonals are equal.
(d) All sides are equal.

Answer 1

Answer:

b)is the correct answer

Step-by-step explanation:

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Answer 2

Final Answer:

The false statements for a rectangle are the following

(a) All rectangles are squares.

(b) Its diagonals are perpendicular.

(d) All sides are equal.

Given:

The statements for the rectangle are as follows.

(a) All rectangles are squares.

(b) Its diagonals are perpendicular.

(c) Its diagonals are equal.

(d) All sides are equal.

To Find:

The false statements among the given ones are to be marked.

Explanation:

The following points are necessary for this solution.

• The rectangle and the square are both quadrilaterals as each of them has four edges and four vertices.
• Both the rectangle and the square are parallelograms as their opposite sides are parallel and equal to each other.
• Each of the four interior angles in the rectangle and the square is a right angle.
• A rectangle has its opposite sides equal to each other, but its adjacent sides are unequal.
• A square has its all sides equal to each other.

Step 1 of 4

The statement (a) of the given problem is false.

By definition, a square is a rectangle but every rectangle is not a square.

Step 2 of 4

Here, statement (b) is false. The diagonals of a rectangular are not perpendicular.

Step 3 of 4

The statement (c) of the given problem is true.

The diagonals are equal to each other in a rectangle.

Step 4 of 4

The given statement (d) is false, as discussed above.

Therefore, the required false statements are all the stated ones, except statement c.

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