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a n s w e r all from the second- Part II: Angles in triangles in a
The investigations consist two main parts: I.II. Geometric constructions using straightedge and compassAngles in triangles in a circle. Your submission must be authentic and clearly scanned. Part I: Geometric constructions We begin by learning (or relearning) how to draw lines and circles using only a compass and astraightedge. Geometrical constructions DO NOT necessitate the use of a protractor to measure anglesor a ruler to measure lengths. This may seem daunting initially but instantly becomes very interestingonce you’ve learnt how to construct them.The following website helps you to learn some of these constructions.https://www.mathopenref.com/constructions.htmlMore specifically, you need to demonstrate that you are able to construct the following on blank A4papers (not lined or graph). Each construction will need to satisfy the following conditions:- Take up about half the space on a page- Straight lines drawn with a sharp pencil- Construction markings (by use of pencil with a compass) must be shown- Hand-drawn and not photocopiedNo. Constructions Reference video guide 1 Perpendicular bisector of a linesegment https://www.mathopenref.com/constbisectline.html 2 Dividing a segment into n equal parts https://www.mathopenref.com/constdividesegment.html 3 Bisecting an angle https://www.mathopenref.com/constbisectangle.html 4 Construct a 45o angle https://www.mathopenref.com/constangle45.html 5 Construct a 60o angle https://www.mathopenref.com/constangle60.html 6• 30-60-90 triangle, given thehypotenuse https://www.mathopenref.com/const306090.html Part II: Angles in triangles in a circleAll constructions are to be drawn on blank A4 papers.For this task, first construct a circle with 6 points evenly spaced and marked along the circumference. Dothis using your compass only. Construction markings should be seen clearly. Think about how you cando it and try it out a couple of times if necessary before you draw a good one. It might look somethinglike this one below. Next, using your ruler, using any of the points on the circle, draw one possible triangle. Determine theangles in this triangle without using a protractor.After this, replicate more 6-point circles to draw at least 3 more different triangles. Again, measure theangles in each triangle without the use of a protractor.Answer the following questions based on your investigations. Justify your answers with clearexplanations that incorporate your diagrams.1. What kinds of triangle can be drawn? Name their properties.2. How many different triangles are there?3. What are their angles (for each triangle you constructed)?4. What might be inferred about triangles with right-angles in them?5. What is the largest angle that can be found in such triangles?6. What is the smallest angle that can be found in such triangles?7. What difference would it make if the centre of the circle were allowed as one vertex of a triangle?8. What can be said about all such triangles drawn in the 6-point circle? Now, construct 8-point circles and explore at least 4 triangles.Answer the following questions based on your investigations, again with justifying explanations.9. Under what conditions are your triangles obtuse-angled?10. Under what conditions are your triangles acute-angled?11. How many different triangles can you get on an n-point circle? The Geogebra Geometry online tool (https://www.geogebra.org/geometry?lang=en-AU) is useful formore exploration.
