Math Labs with Activity – Verify the Properties of the Sides and Angles of a Parallelogram
To verify the parallelogram properties of the sides and angles of a Parallelogram.
- A sheet of white paper
- A geometry box
- A sheet of tracing paper
By geometry, we know that in a parallelogram
- opposite sides are equal, and
- opposite angles are equal.
Step 1: Construct a parallelogram ABCD on the sheet of white paper.
Step 2: Draw the diagonal AC of the parallelogram as shown in Figure 20.1.
Step 3: Trace the ΔABC on the tracing paper. Label the triangle obtained on the tracing paper as ΔA’B’C’. Shade ΔA’B’C’. Rotate the tracing paper and place ΔA’B’C’ over ΔACD as shown in Figure 20.2. Record your observations.
We observe that ΔA’B’C’ exactly covers ΔACD.
Therefore, ΔA’B’C’ is congruent to ΔACD and so ΔABC is congruent to ΔACD.
Hence, AB =CD,
BC =AD, and ∠B = ∠D.
(Similarly, we can show that ∠A = ∠C.)
Conclusions We conclude that in a parallelogram, the opposite sides are equal and the opposite angles are equal.
It is verified that in a parallelogram the opposite sides are equal and the opposite angles are equal.