Question 4 4.1 State four differences between inductive and deductive reasoning in geometry (4) 4.2 Complete the following table about the Van Hiele levels of geometric knowledge. (10) Level of knowledge and understanding Visualisation Analysis 4.2.5 427 4 2.9 Description 421 4.2.3 See the interrelationships between figures Construct proofs rather than memorise them; see the possibility of developing one proof in more than one way See the construction of geometric systems Teacher activity 4.2.2 424 4 2.6 4.2.8 4 2.10 [14]
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4.1. Quadrilateral HAND has vertices H (-5, -1); A (7, 1); N (6, 7) and D (-6, 5). 4.1.1. Is the quadrilateral HAND a parallelogram, a rectangle or neither? 4.1.2. Explain your answer to question 4.1.1. 4.1.3. Find the midpoint of each diagonal. 4.1.4. What is your conjecture about your solution to question 4.1.3? 4.2. In the diagram, center C of the circle lies on the straight line 3x + 4y + 7 = 0. The straight line cuts the circle at D and E (-1, -1). The circle touches the y-axis at P (0, 2). 4.2.1 Formulate FOUR questions that Grade 12 students can be asked about this diagram to test their knowledge of geometry. Show how a learner should respond to the four questions and show ALL the steps (solve the problems).
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Developing Proof In Exercises $1-4,$ the four conjectures are consequences of the Inscribed Angle Conjecture. Prove each conjecture by writing a paragraph proof or a flowchart proof. Use reasoning strategies, such as think backwards, apply previous conjectures and definitions, and break a problem into parts to develop your proofs. The opposite angles of a cyclic quadrilateral are supplementary. Given: Circle $O$ with inscribed quadrilateral $L I C Y$ Show: $\angle L$ and $\angle C$ are supplementary (GRAPH CANT COPY)
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20. The type of reasoning where a person makes conclusions based on observations and patterns is called A. Inductive reasoning B. Deductive reasoning C. Conjecture D. Experiments 21. Which number is a counterexample to the following statement? All numbers that are divisible by 2 are divisible by 4. A. 0 B. 28 C. 12 D. 42 22. A researcher observes that more acts of vandalism are committed by same-sex gangs than by mixed-sex gangs. She theorizes that competition for recognition among equal-status peers increases the tendency to commit publicly deviant acts. What type(s) of reasoning is this? A. inductive reasoning B. deductive reasoning C. neither inductive nor deductive reasoning D. both inductive and deductive reasoning 23. Find the next 3 numbers in the pattern: 2, 12, 72, ... A. 432, 2592, 15554 B. 432, 2592, 15552 C. 144, 288, 576 D. 78, 84, 90
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