1. **Problem Statement:** Complete the table about Van Hiele levels of geometric knowledge and understanding, state differences between inductive and deductive reasoning in Geometry, and state five Euclid’s postulates with discussion and sketches. 2. **Van Hiele Levels Table Completion:** - Visualisation - Description (1.1.1): Recognising shapes and figures by their appearance. - Teacher activity (1.1.2): Use activities that involve identifying shapes and naming them. - Analysis - Description (1.1.3): Recognising properties and components of shapes. - Teacher activity (1.1.4): Guide students to analyze properties like angles and sides. - Informal Deduction - Description (1.1.5): See the interrelationships between figures. - Teacher activity (1.1.6): Encourage students to compare and relate different figures. - Formal Deduction - Description (1.1.7): Construct proofs rather than memorise them; see the possibility of developing one proof in more than one way. - Teacher activity (1.1.8): Teach formal proof writing and multiple proof strategies. - Rigor - Description (1.1.9): See the construction of geometric systems. - Teacher activity (1.1.10): Introduce axiomatic systems and advanced geometry concepts. 3. **Differences between Inductive and Deductive Reasoning in Geometry:** - Inductive reasoning involves observing specific cases and making generalizations. - Deductive reasoning starts with general axioms or postulates and derives specific conclusions logically. 4. **Five Euclid’s Postulates with Discussion and Sketches:** - Postulate 1: A straight line segment can be drawn joining any two points. - Sketch: Two points connected by a straight line. - Postulate 2: A straight line segment can be extended indefinitely in a straight line. - Sketch: A line segment extended beyond its endpoints. - Postulate 3: A circle can be drawn with any center and radius. - Sketch: Circle with center and radius marked. - Postulate 4: All right angles are equal to one another. - Sketch: Two right angles shown as equal. - Postulate 5 (Parallel Postulate): If a line intersects two lines such that the interior angles on the same side are less than two right angles, the two lines, if extended indefinitely, meet on that side. - Sketch: Two lines and a transversal illustrating the interior angles. Each postulate forms the foundation of Euclidean geometry and is used to prove further geometric theorems. Final answers are the completed table entries, the reasoning differences, and the five postulates with explanations and sketches.