Draw a regular polygon of 4 sides. Using angle tool measure 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.
Task 2
Observe the corresponding values in columns 2 and 4 carefully. Do you notice any pattern? Write down what you observe.
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.
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Verify the rule for a regular polygon of
i) 10 sides
ii) 20 sides.
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 angles measuring less than 180 degrees).
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)
[Contributed by administrator on 10. Januar 2018 21:42:17]
Activity 2: Angle sum property of polygons
Task 1
Draw a regular polygon of 4 sides. Using angle tool measure 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.
Task 2
Observe the corresponding values in columns 2 and 4 carefully. Do you notice any pattern? Write down what you observe.
__________________________________________________________________________________
__________________________________________________________________________________
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.
__________________________________________________________________________________
__________________________________________________________________________________
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 angles measuring less than 180 degrees).
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)