To draw the trapezium $ABCD$, where:

• $AB \parallel DC$
• $AB = 7 \, \text{cm}$
• $BC = 5 \, \text{cm}$
• $AD = 6.5 \, \text{cm}$
• $\angle B = 60^\circ$

Here's a step-by-step guide:

1. Draw line segment AB:

• Start by drawing a horizontal line $AB$ of length $7 \, \text{cm}$. Label the endpoints as $A$ and $B$.

2. Construct $\angle B = 60^\circ$:

• From point $B$, draw a line at a $60^\circ$ angle to the line $AB$.
• The length of this line segment should be $5 \, \text{cm}$, as given by $BC$.

3. Mark point C:

• The point where this line intersects will be labeled as point $C$. So, $BC = 5 \, \text{cm}$.

4. Draw AD:

• From point $A$, draw a line of length $6.5 \, \text{cm}$ to form the line segment $AD$.

5. Draw DC parallel to AB:

• Now, using the fact that $AB \parallel DC$, you will need to draw line segment $DC$ parallel to $AB$, and make sure that the trapezium has its sides properly connected.

This procedure will give you the trapezium $ABCD$.

Would you like a more detailed explanation or visual representation of any part of the process?

Related Questions:

1. How do you calculate the height of a trapezium given its sides and angles?
2. How can you verify that the lines $AB$ and $DC$ are parallel after constructing the trapezium?
3. What is the area formula for a trapezium and how do you apply it here?
4. How do the angles of a trapezium relate to its sides and parallelism?
5. What are the properties of a trapezium, and how do they help in construction?

Tip: Always check that the parallel sides are truly parallel using a protractor or by checking corresponding angles when constructing shapes like trapeziums.