Extended Geometry

Topics

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Sample objectives

What this unit covers

• Geometrical terms: Utilize and understand the following geometrical terms: point, vertex, line, plane, parallel, perpendicular, perpendicular bisector, bearing, right angle, acute, obtuse, and reflex angles, interior and exterior angles, similar, congruent, and scale factor. Additionally, comprehend the vocabulary related to triangles (equilateral, isosceles, scalene, right-angled), special quadrilaterals (square, rectangle, kite, rhombus, parallelogram, trapezium), polygons (regular and irregular polygons, pentagon, hexagon, octagon, decagon), and solids (cube, cuboid, prism, cylinder, pyramid, cone, sphere, hemisphere, frustum, face, surface, edge). Furthermore, grasp the vocabulary associated with circles, including centre, radius (plural: radii), diameter, circumference, semicircle, chord, tangent, major and minor arc, sector, and segment.
• Similarity: 1 Determine the lengths of similar figures. 2 Apply the relationships between lengths and areas, including the use of scale factors for similar shapes and their corresponding surface areas. 3 Calculate the volumes of similar solids using the relationship between their lengths. 4 Solve problems related to similarity and provide straightforward explanations, including demonstrating that two triangles are similar using geometric reasoning.
• Symmetry: Identify line symmetry and the order of rotational symmetry for various shapes, including triangles and quadrilaterals, as well as understanding the symmetry properties of three-dimensional shapes like prisms, cylinders, pyramids, and cones, including their planes and axes of symmetry.
• Circle theorems I: Determine unknown angles and provide justifications using the following circle properties: the angle in a semicircle is 90°, the angle between a tangent and a radius is 90°, the angle at the center is double that at the circumference, angles in the same segment are equal, the opposite angles of a cyclic quadrilateral add up to 180°, and the alternate segment theorem.
• Circle theorems II: Understand and apply the symmetry properties of circles, including that equal chords are at the same distance from the center, the perpendicular bisector of a chord goes through the center, and that tangents drawn from a point outside the circle are of equal length. Use these properties to justify answers in geometrical problems.