Exercise 8.6 Solutions

Construct (Page 211)

House Construction Recreate the figure with all sides 5 cm.

Solution:

1. Base: Draw square $BCDE$ with side 5 cm.
   • Draw $CD = 5$ cm.
   • Construct perpendiculars at $C$ and $D$.
   • Mark $CB = 5$ cm and $DE = 5$ cm.
   • Join $BE$.
2. Roof: We need point $A$ such that $AB = 5$ cm and $AE = 5$ cm (assuming roof connects to top corners).
   • Wait, diagram shows the roof on top of side $BC$? No, usually roof is on top. Based on text labels $B, C, D, E$, let’s assume $BC$ is the top side of a square.
   • Draw arcs of radius 5 cm from $B$ and $C$.
   • Intersection is $A$.
   • Join $AB$ and $AC$.

Q3. Is there a 4-sided figure where all sides are equal but it is not a square?

Answer: Yes, a Rhombus.

• A rhombus has 4 equal sides.
• However, its angles do not have to be $90^\circ$.
• Construction: Draw a base $AB$. Draw $AD$ at an angle (say $60^\circ$) with length equal to $AB$. Complete the parallelogram using compass arcs of the same length from $B$ and $D$.

Bigger House (Page 215)

Q1. Construct a bigger house with sides 7 cm. Solution: Follow the exact same steps as the 5 cm house, simply changing the ruler length and compass radius to 7 cm.

Q2. Recreate “Eyes” Solution:

1. Draw a horizontal line of length, say, 6 cm ($AB$).
2. Mark a point $P$ above the line on the perpendicular bisector.
3. Place compass at $P$, adjust radius to pass through $A$ and $B$. Draw the upper arc.
4. Mark a point $Q$ below the line (same distance as $P$).
5. Place compass at $Q$, draw the lower arc connecting $A$ and $B$.