Exercise 8.2 Solutions

Naming Squares (Page 193)

Question: Which of the following is not a name for this square (PQRS)?

1. PQSR
2. SPQR
3. RSPQ
4. QRSP

Answer: 1. PQSR

• Reason: When naming a polygon, vertices must be listed in consecutive order (perimeter). $PQSR$ jumps from $Q$ to $S$ diagonally, which breaks the order. The other three follow the cyclic order.

Figure it Out (Page 194)

Q1. Draw the rectangle and four squares configuration on dot paper. (Practical activity - ensure squares are tilted symmetrically).

Q2. Identify if there are any squares in this collection. Answer: Yes, the rotated figure labeled A is a square. Even though it is rotated, its sides are equal (based on the dot spacing) and its corners form $90^\circ$ angles.

Think: Is it possible to reason out if sides are equal/angles are right without instruments? Answer: Yes, on a dot grid (lattice), you can count “steps” (e.g., 2 units right, 2 units up) to verify lengths and slopes. If the slopes are negative reciprocals, the lines are perpendicular.

Q3. Draw at least 3 rotated squares and rectangles. (Self-verification: Ensure opposite sides are parallel and adjacent sides are perpendicular).