Square. Solve - Give reasons.

In a square, all four sides are equal in length. The given length for side NM is $40 \text{ mm}$.
Therefore:

$$KL = 40 \text{ mm} \quad (\text{Reason: All sides of a square are equal})$$ $$LM = 40 \text{ mm} \quad (\text{Reason: All sides of a square are equal})$$ $$KN = 40 \text{ mm} \quad (\text{Reason: All sides of a square are equal})$$

In a square, all interior angles are right angles, meaning they each measure $90^\circ$.
Therefore:

$$\hat{K} = 90^\circ \quad (\text{Reason: All angles of a square are } 90^\circ)$$ $$\hat{L} = 90^\circ \quad (\text{Reason: All angles of a square are } 90^\circ)$$ $$\hat{M} = 90^\circ \quad (\text{Reason: All angles of a square are } 90^\circ)$$ $$\hat{N} = 90^\circ \quad (\text{Reason: All angles of a square are } 90^\circ)$$

Summary of answers:

• $KL = \boxed{\text{40 mm}}$
• $LM = \boxed{\text{40 mm}}$
• $KN = \boxed{\text{40 mm}}$
• $\hat{K} = \boxed{90^\circ}$
• $\hat{L} = \boxed{90^\circ}$
• $\hat{M} = \boxed{90^\circ}$
• $\hat{N} = \boxed{90^\circ}$