Exercise 8.3 Solutions

Construct (Page 197)

Q1. Draw a rectangle with sides of length 4 cm and 6 cm.

Solution:

1. Draw $AB = 6$ cm.
2. At $A$ and $B$, construct vertical perpendiculars.
3. Mark $AD = 4$ cm and $BC = 4$ cm on these perpendiculars.
4. Join $C$ and $D$.
5. Check: Measure $CD$. It should be 6 cm. Measure angles $\angle C$ and $\angle D$. They should be $90^\circ$.

Q2. Draw a rectangle of sides 2 cm and 10 cm.

Solution: Follow the same method as above. The rectangle will be long and thin.

• Sides: $PQ = 10$ cm, $PS = 2$ cm.

Q3. Is it possible to construct a 4-sided figure where all angles are $90^\circ$ but opposite sides are NOT equal?

Answer: No. If a quadrilateral has three $90^\circ$ angles, the fourth must be $90^\circ$ (since sum is $360^\circ$). A quadrilateral with four right angles is a rectangle (or square). By definition of a rectangle, opposite sides must be equal.

Exercise 8.4 Exploration (Page 198)

Data Table: Looking at distances of $X$ from $A$ and $Y$ from $B$.

Observation:

1. Length XY: If $X$ and $Y$ move the same distance from $A$ and $B$, then $XY$ remains parallel to $AB$ and equal in length to $AB$.
2. Shape: The figure $ABYX$ is a rectangle.