Question

4. Complete Activity 2: To prove that the pairs of vertically opposite angles are equal by
cutting and pasting method on an A4 size sheet​

Answer 1

Answer:

Objective

To verify that the opposite angles of a cyclic quadrilateral are supplementary by paper folding activity.

Materials Required

White paper sheet, compass, glazed papers, pencil, a pair of scissors, gluestick.

Procedure

Draw a circle of radius 2 cm on a white glazed paper with centre O.

Cut this circle with centre O and draw one more circle of same radius.

Take any four points A, B, C, D on the circumference of both the circles.

Join AB, BC, CD, DA by paper folding on the both the circles.

We get a cyclic quadrilateral ABCD on both the circles

Take ∠A and ∠C of blue colour and ∠B and ∠D of pink colour in both circles.

From the second circle, using transparent sheets make cut outs of ∠A, ∠B, ∠C, ∠D.

. Take ∠A and ∠C of blue colour and ∠B and ∠D of pink colour.

Make a straight line on white paper sheet. Place cut outs of ∠A and ∠C adjacent to each other on a straight line and paste them

Take cut outs of ∠B and ∠D and place them adjacent to each other on another straight line and paste them

Observation

As ∠A and ∠C forms a linear pair.

∴ ∠A + ∠C = 180°

Similarly, ∠B + ∠D = 180°

Result

Hence, it is verified that in a cyclic quadrilateral, sum of opposite angles is 180°.