Question

Of the following two statements , which is a good definition ? Explain . " A rectangle is a parallelogram with 4 right angles . " " A rectangle is a parallelogram . " The first statement ; it is reversible . B. The first statement , a rectangle can either be a parallelogram , or it can have four right angles . The second statement all parallelograms are also rectangles . D. The second statement : a rectangle is always a parallelogram , but it may not have exactly four right angles .

Answer 1

This is about understanding the meaning of a rectangle and parallelogram.

Option A is the correct definition.

We are given the 2 statements as;

1)  A rectangle is a parallelogram with 4 right angles

2) A rectangle is a parallelogram

• Let us define a rectangle and parallelogram;

- A rectangle is defined as a quadrilateral with four right angles. This means all the angles are equal. It also has 4 sides with the length of opposite sides being parallel to each other.

- A parallelogram is defined as a quadrilateral that has two pairs of parallel sides with the opposite sides of such parallelogram having equal length and the opposite angles being equal.

• Option A; This is correct because the reverse statement is that; A parallelogram is a rectangle with 4 right angles, This is possible because the only condition where a parallelogram is a rectangle is when it has 4 right angles.

• Option B; This is wrong because a rectangle is not a parallelogram.

• Option C; This is wrong because not all parallelograms are rectangles.

• Option D; This is wrong because a rectangle must have 4 right angles

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