Question

What is the correct order of reasons that complete the proof? a. definition of congruence; distance formula; if two consecutive sides of a rectangle are congruent, then it’s a square b. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it’s a square c. distance formula; if two consecutive sides of a rectangle are congruent, then it’s a square; definition of congruence d. if two consecutive sides of a rectangle are congruent, then it’s a square; distance formula; definition of congruence

Answer 1

The correct order of reasoning in a proof to show that a rectangle is a square involves using the distance formula to find the lengths, applying the definition of congruence to compare side lengths, and then concluding with the property that congruent consecutive sides indicate a square, hence option b is correct.

Step-by-step explanation:

The question you've asked concerns the process involved in proving that a rectangle is a square using geometrical concepts. When setting out to prove such a geometric statement regarding a rectangle being a square, an expected order of reasoning would typically involve:

The correct sequence of these statements, which completes the proof logically, would be option b: distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it’s a square. This sequence is logical because it starts by finding the actual lengths, compares them for congruence, and then applies the specific property of squares to finalize the proof. No other sequence would correctly match the logical flow required for a rigorous proof.

Answer 2

The correct sequence for the proof starts with the distance formula, followed by the definition of congruence, and ends with the property that states if two consecutive sides of a rectangle are congruent, then it is a square.

Step-by-step explanation:

The correct order of reasons that complete the proof for determining whether a rectangle is a square by using the properties of congruence and the distance formula must be logical and sequential. Therefore, the correct sequence is as follows:

Use the distance formula to determine the lengths of the sides of the rectangle.

Apply the definition of congruence to show that the sides are congruent if they have the same length.

Finally, use the property that if two consecutive sides of a rectangle are congruent, then it’s a square.

So the correct order of reasons is distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it’s a square.