Lab Manual: Cyclic Quadrilateral - Class 10 PDF Download

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Objective

• the opposite angles of a cyclic quadrilateral are supplementary, and
• if one side of a cyclic quadrilateral is produced then the exterior angle is equal to the opposite interior angle.

Materials Required
A piece of cardboard, A sheet of white paper, A sheet of glazed paper, A sheet of tracing paper, A geometry box, A pair of scissors, A tube of glue

Theory

Procedure

Draw a circle of any radius on this sheet and also draw a cyclic quadrilateral ABCD.
Step 2: Produce the side CD of the cyclic quadrilateral ABCD to E. Mark the exterior angle ∠ADE (see Figure 29.1).

Step 3: Make an exact replica of the quadrilateral ABCD on a glazed paper using the tracing paper. Also, make a replica of ∠ADE on the tracing paper.
Step 4: Cut out the quadrilateral ABCD made on the sheet of glazed paper and further cut it into four parts such that each part contains one of the angles ∠A, ∠B, ∠C and ∠D (see Figure 29.2)

Step 5: Place ∠A and ∠C adjacent to each other (as in Figure 29.3).’What do you observe?

Step 6: Place ∠B and ∠D adjacent to each other (as in Figure 29.4). What do you observe?

Step 7: Place the replica of ∠ADE (which you have on the tracing paper) on ∠B of the quadrilateral ABCD on the sheet of white paper. What do you observe?

Observations

• When ∠A and ∠C are placed adjacent to each other, they form a linear pair, i.e., ∠A + ∠C = 180°.
• When ∠B and ∠D are placed adjacent to each other, they form a linear pair, i.e., ∠B + ∠D = 180°.
• When ∠ADE is placed over ∠B, it covers ∠B completely, i.e., ∠ADE = ∠B.

Result
It is verified that

• the opposite angles of a cyclic quadrilateral are supplementary, and
• if one side of a cyclic quadrilateral is produced then the exterior angle is equal to the opposite interior angle.

Remarks
The above results are true only for a cyclic quadrilateral.