Verify experimentally that the opposite angles of a cyclic quadrilateral are supplementary
To verify experimentally that the opposite angles of a cyclic quadrilateral are supplementary, we can follow these steps:
Step 1: Draw a cyclic quadrilateral. A cyclic quadrilateral is a quadrilateral whose vertices lie on a circle.
Step 2: Measure the four angles of the quadrilateral using a protractor.
Step 3: Calculate the sum of opposite angles. Add together the measures of one pair of opposite angles of the quadrilateral.
Step 4: Compare the calculated sum with the sum of the other pair of opposite angles.
Step 5: Repeat steps 3 and 4 for multiple examples of cyclic quadrilaterals to confirm that in each case, the opposite angles are supplementary.
Let's consider an example:
1. Draw a circle using a compass and mark four points on the circumference to define the vertices of the quadrilateral.
2. Connect the four points to form the quadrilateral.
3. Measure the four angles of the quadrilateral using a protractor and record their measurements.
4. Add the measurements of one pair of opposite angles and calculate their sum.
5. Add the measurements of the other pair of opposite angles and calculate their sum.
6. Compare the two sums. If they are approximately equal (accounting for measurement errors), then it confirms that the opposite angles are supplementary.
Repeat this process for different examples of cyclic quadrilaterals, and you will find that in each case, the opposite angles are supplementary, supporting the experimental verification.