Answer: A shape is a rectangle if and only if the shape has exactly four sides and four right angles.
Step-by-step explanation:
- If both a conditional statement and its converse statement is true then we write a combine form of both the statements known as a bi-conditional statement. It is written in the if and only if form.
From the given options only option one is correct because it is true from both ways.
It can be written as If a shape has exactly four sides and four right angles then the shape is a rectangle.
- A shape is a trapezoid if and only if the shape has a pair of parallel sides.
It is not true because a if the shape has a pair of parallel sides then it can be a parallelogram.
- A shape is a triangle if and only if the shape has three sides and three acute angles.
It is not true because a if the shape has three sides and three acute angles then it is only a acute triangle.
- A shape is a square if and only if the shape has exactly four congruent sides.
It is not true because if the shape has exactly four congruent sides then it can also be rhombus.
So the only true bi-conditional statement is "A shape is a rectangle if and only if the shape has exactly four sides and four right angles.
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