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@This document (2.2 Angle sum property of polygons) is re-created by administrator on 17 May 2017
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"content": "GEOMETRIC REASONING\u200b\r\nAngle Sum Property of Polygons
\r\n\r\n
Task 1\r\n\r\n
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.
\r\n
\r\nRepeat this task for regular polygons with 5, 6, 7 sides, and complete the table. The first row is done as an example.
\r\n
\r\nNOTE: The above activity is to be on GeoGebra software installed on your computer
\r\n![\"me_U05A03Q01_en_img01\"](\"/media/8/1/f/ff3a11a5e8f4d9202a3352ccaca3c5e6706ad5da588d9747bdd7726136339.png\")
\r\n![\"me_U05A03Q01_en_img02\"](\"/media/3/e/1/9e1a72ac9ed6450b0e2cacaba879974a2eee255b26ae6af213f9785ee938e.png\")
\r\n(Click here to write)
\r\n![\"Enter\"](\"/media/7/1/2/3c5e1f84967ec527bd5bebbd2ce3b8208a4a417a1c3c6bb94d2cc0d34130b.svg\")
\r\n \r\n
Task 2\r\n\r\n
\r\nObserve the corresponding values in columns 2 and 4 carefully. Do you notice any pattern? Write down what you observe.
\r\n\r\n(Click here to write)
\r\n
\r\n \r\n
Task 3\r\n\r\n
\r\nBased 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.
\r\n\r\n(Click here to write)
\r\n\r\n\r\n
\r\nVerify the rule for a regular polygon of
\r\n i) 10 sides
\r\n ii) 20 sides.
\r\n(Click here to write)
\r\n
\r\n \r\n
Task 4\r\n\r\n
\r\nDo 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.
\r\n\r\n(A convex polygon has all angles measuring less than 180 degrees).
\r\n![\"me_U05A03Q04_en_img03\"](\"/media/a/a/8/400e7f0ffc4115527cfe97a91632c6009e25052bf4b48a131e6e616731391.png\")
\r\n(Click here to write)
\r\n
\r\n \r\n
Extension Task 1\r\n\r\n
\r\nDo you think the rule will hold true for polygons that are concave? Verify it, and record your observations and findings.
\r\n
\r\n(A concave polygon contains at least one reflex angle)
\r\n\r\n
\r\n(Click here to write)
\r\n",
"content_org": "GEOMETRIC REASONING\u200b\r\nExploring Angle Sum Property of Polygons
\r\n\r\n
\r\nTask 1
\r\n\r\n
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.
\r\n
\r\nRepeat this task for regular polygons with 5, 6, 7 sides, and complete the table. The first row is done as an example.
\r\n
\r\n\r\n
\r\nTask 2
\r\n\r\n
\r\nObserve the corresponding values in columns 2 and 4 carefully. Do you notice any pattern? Write down what you observe.
\r\n
\r\n__________________________________________________________________________________
\r\n
\r\n__________________________________________________________________________________
\r\n \r\nTask 3
\r\n\r\n
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.
\r\n __________________________________________________________________________________
\r\n
\r\n__________________________________________________________________________________\r\n\r\nVerify the rule for a regular polygon of
\r\n i) 10 sides
\r\n ii) 20 sides.
\r\n
\r\n\r\n
\r\nTask 4
\r\n\r\n
\r\nDo 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.
\r\n
\r\n(A convex polygon has all angles measuring less than 180 degrees).
\r\n![\"L12img5\"](\"http://clixplatform.tiss.edu/media/a/a/8/400e7f0ffc4115527cfe97a91632c6009e25052bf4b48a131e6e616731391.png\")
\r\n
\r\nExtension Task 1
\r\n\r\n
Do you think the rule will hold true for polygons that are concave? Verify it, and record your observations and findings.
\r\n
\r\n(A concave polygon contains at least one reflex angle)\r\n\r\n
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