Task 1Draw a regular polygon of four sides. Measure the interior angles of the polygon. Fill in the relevant columns in the table below.
NOTE: The above activity is to be done on GeoGebra software using the angle measurement tool.
Now using line segment tool, divide it into non-overlapping triangles, (one is shown for you) and fill the table.
Repeat this task for regular polygons with 5, 6, 7 sides, and complete the table. The first row is done as an example.
(Click here to write)
Task 2
Observe the corresponding values in columns 2 and 4 carefully. Do you notice any pattern? Write down what you observe.
(Click here to write)
Task 3
Based on the patterns observed, come up with a general rule that would give the sum of angles in a regular polygon of n sides. Justify your rule.
(Click here to write)
Verify the rule for a regular polygon of
i) 10 sides
ii) 20 sides. (Click here to write)
Task 4
Do you think the above rule will hold true for other polygons, which are not regular? Verify for convex polygons. Enter the details of your constructions in the table below.
(A convex polygon has all interior angles measuring less than 180 degrees).
(Click here to write)
Extension Task 1
Do you think the rule will hold true for polygons that are concave? Verify it, and record your observations and findings.
(A concave polygon contains at least one reflex angle)
(Click here to write)
[Contributed by administrator on 25. Februar 2025 10:32:49]
Angle Sum Property of Polygons
Task 1
Draw a regular polygon of four sides. Measure the interior angles of the polygon. Fill in the relevant columns in the table below.
Now using line segment tool, divide it into non-overlapping triangles, (one is shown for you) and fill the table.
Repeat this task for regular polygons with 5, 6, 7 sides, and complete the table. The first row is done as an example.
(Click here to write)
Task 2
Observe the corresponding values in columns 2 and 4 carefully. Do you notice any pattern? Write down what you observe.
(Click here to write)
Task 3
Based on the patterns observed, come up with a general rule that would give the sum of angles in a regular polygon of n sides. Justify your rule.
(Click here to write)
Verify the rule for a regular polygon of
i) 10 sides
ii) 20 sides.
(Click here to write)
Task 4
Do you think the above rule will hold true for other polygons, which are not regular? Verify for convex polygons. Enter the details of your constructions in the table below.
(A convex polygon has all interior angles measuring less than 180 degrees).
(Click here to write)
Extension Task 1
Do you think the rule will hold true for polygons that are concave? Verify it, and record your observations and findings.
(A concave polygon contains at least one reflex angle)
(Click here to write)