Question

To verify that in a triangle, the line joining the mid-
points of any two sides is parallel to the third side

and half of it by paper folding and pasting.

Answer 1

Step-by-step explanation:

Theory

Midpoint theorem: The line segment joining the midpoints of any two sides of a triangle is parallel to the third side.

Procedure

Step 1: Paste one sheet of white paper on the cardboard.

Draw a ΔABC on this paper.

Step 2: Mark the midpoints D and E of the sides AB and AC respectively (the midpoints of the sides can be obtained by the method of paper folding). Join D and E. Blacken ΔADE with the marker pen.

Step 3: Cut another triangle CEE from the other sheet of white paper so that ΔCEE is congruent to ΔADR Blacken ΔCEE with the marker pen.

Math Labs with Activity - Verify the Midpoint Theorem 1

Observations

Since ΔCEF is congruent to ΔADE, therefore DE = £F.

Measure DE and BC. We find that DE = ½ BC.

From (i) and (ii), we derive that DF = BC.

Since ΔCEF is congruent to ΔADE, therefore AD = FC.

Since D is the midpoint of AB, we have AD = DB.

From (i) and (ii), we get FC = DB.

From the above observations, it is clear that DFCB is a parallelogram.

Hence, DE || BC.

Result

The midpoint theorem is verified.