Question

Statement 1: Given only the length of a diagonal of a square, a unique square can be drawn.

Statement 2: Given only the length of a side of a rhombus, a unique rhombus can be drawn.

• A. Both statement 1 and statement 2 are true
• B. Statement 1 is true, while statement 2 is false.
• C. Statement 1 is false, while statement 2 is true.
• D. Both statement 1 and statement 2 are false.

Answer 1

The correct option is B Statement 1 is true, while statement 2 is false.

Given the length of a diagonal of a square, we can calculate the length of the sides of the square. Further, since the angles of a square are known, a unique square can be drawn.

However, if only the measure of a side of a rhombus is given, an infinite number of rhombi can be drawn with varying interior angles.

Thus, statement 1 is true while statement 2 is false.