# Math Labs with Activity – Verify the Properties of a Trapezium

## Math Labs with Activity – Verify the Properties of a Trapezium

OBJECTIVE

To verify the properties of a trapezium

Materials Required

1. Two sheets of white paper
2. A geometry box
3. A pair of scissors
4. A tube of glue

Theory
By geometry, we know that in a trapezium ABCD, if AB || DC and E and F are the midpoints of the sides AD and BC respectively then

1. EE || AB, and
2. EF = ½(AB+DC).

Procedure
Step 1: Construct a trapezium ABCD (in which AB || DC)
on a sheet of white paper. Mark the midpoints E and F of the non-parallel sides AD and BC respectively (the midpoints of the sides can be obtained by the method of paper folding). Join EE (see Figure 24.1).

Step 2: Mark the angles in the diagram as shown in Figure 24.2.

Step 3: Paste the two quadrilaterals ABFE and EFCD as shown in Figure 24.3.

Observations and Calculations

1. In Figure 24.2, for the trapezium ABCD we have AB || DC.
∴ ∠5 + ∠8 = 180° (consecutive interior angles) and so, in Figure 24.3, ∠5 and ∠8 form a linear pair, i.e., AD’ is a straight line.
Also, in Figure 24.2 we have ∠6 + ∠7 = 180° (since ∠6 and ∠7 form a linear pair) and so, in Figure 24.3, ∠6 and ∠7 form a linear pair, i.e., EE’ is a straight line.
2. In Figure 24.2, for the trapezium ABCD we have AB || DC.
∠1 + ∠4 = 180° (consecutive interior angles) and so, in Figure 24.3, AE || E’D’ (since ∠1 and ∠4 are consecutive interior angles).
3. In Figure 24.2, we have AE = ED (∴ E is the midpoint of AD) in Figure 24.3, we have AE=E’D’ (since E’D’=ED).
Thus, we have AE || E’D’ and AE =E’D’.
Hence, the quadrilateral AD’E’E is a parallelogram (a pair of opposite sides being equal and parallel).
4. AD’E’E being a parallelogram, we have