주제 / GCSE / Mathematics / Geometry and measures Geometric language, 2D and 3D shapes 플레이하며 배우기
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교육자를 위해: Geometric language, 2D and 3D shapes(Mathematics, Geometry and measures)을(를) 위한 바로 쓸 수 있는 수업 슬라이드, 복습 노트 — 수업에 사용하거나, 학습자들이 실시간 게임으로 즐기는 인터랙티브 클래스 활동으로 진행하세요.
수업 노트 Key Geometric Terms and Notation Point : an exact location, named with a capital letter (e.g., A).Line : a straight path extending infinitely both ways; line segment has two endpoints; ray has one endpoint.Vertex (plural vertices ): a corner where two or more edges meet; edge : a line segment where two faces meet.Plane : a flat surface that extends infinitely; a face of a 3D shape lies in a plane.Parallel lines are distinct coplanar lines that never meet. Perpendicular lines meet at 90°, marked with a small square. Congruent shapes have identical size and shape. Similar shapes have corresponding lengths in a constant ratio; scale factor 1 is allowed. Regular polygon : all sides equal and all interior angles equal.Similar triangles Similar triangles 4 cm 3 cm 5 cm 8 cm 6 cm 10 cm Corresponding lengths are multiplied by 2. Properties of 2D Shapes Triangle types: equilateral (3 equal sides, 3 equal angles), isosceles (2 equal sides, 2 equal angles), scalene (no equal sides), right-angled (one 90° angle).Quadrilateral types: square (4 equal sides, 4 right angles), rectangle (opposite sides equal, 4 right angles), parallelogram (opposite sides parallel and equal), rhombus (4 equal sides, opposite angles equal), trapezium (one pair of parallel sides), kite (two pairs of adjacent equal sides).Polygon naming: 3 sides = triangle, 4 = quadrilateral, 5 = pentagon, 6 = hexagon, 8 = octagon.A regular polygon has all sides and angles equal; e.g., regular hexagon has 6 equal sides and 6 equal angles. Interior angle sum of an n-sided polygon = (n − 2) × 180°.Diagonals : lines connecting non-adjacent vertices; a square has 2 diagonals, a pentagon has 5.Faces, Edges, and Vertices of 3D Shapes Cube : 6 square faces, 12 edges, 8 vertices.Cuboid : 6 rectangular faces (opposite faces equal), 12 edges, 8 vertices.Triangular prism : 5 faces (2 triangles, 3 rectangles), 9 edges, 6 vertices.Cylinder : 2 circular faces and 1 curved surface; 2 edges (circles), 0 vertices.Cone : 1 circular face, 1 curved surface, 1 vertex (apex), 1 curved edge.Sphere : 1 curved surface, 0 edges, 0 vertices.Square-based pyramid : 5 faces (1 square, 4 triangles), 8 edges, 5 vertices.Square-based pyramid Square-based pyramid 5 cm 4 cm slant height = √(5² + 2²) = 5.39 cm Prisms and Pyramids A right prism has a constant polygonal cross-section and rectangular lateral faces. The face, edge and vertex formulas below apply to polygonal prisms. Cuboid and cube are special prisms with rectangular cross-sections.A cylinder has a constant circular cross-section, but it is not a polygonal prism. Pyramid : a solid with a polygon base and triangular faces meeting at a common apex ; named by its base (e.g., square-based pyramid).A cone has a circular base and curved surface meeting at an apex; it is not a polygon-based pyramid. For a prism, number of faces = (number of sides of cross-section) + 2; edges = 3 × (number of sides); vertices = 2 × (number of sides). For a pyramid with an n-sided base: faces = n + 1, edges = 2n, vertices = n + 1. Cylinder: flat and curved surfaces Cylinder: flat and curved surfaces 3 cm 5 cm Nets of 3D Shapes A net is a 2D pattern that folds to form a 3D shape. A cube has 11 different nets; each net has 6 squares arranged so they fold without overlap. To check a net: ensure all faces are present and connected, and that folding along edges produces the correct solid. Common nets: cuboid (6 rectangles), triangular prism (2 triangles + 3 rectangles), square-based pyramid (1 square + 4 triangles). Cylinder net: two circles and a rectangle (curved surface unrolled). Cone net: one circle and a sector of a circle. A net must not have flaps that overlap when folded. A valid cube net A valid cube net surface area = 2(9 + 9 + 9) = 54 cm² Plans and Elevations Plan : the view from directly above (top view).Front elevation : the view from the front.Side elevation : the view from the side (often right side).For a 3D shape made of cubes, draw the outline of each view, showing visible squares. Plan and elevations are 2D drawings that show the shape's dimensions from different directions. Example: a cuboid of length 3, width 2, height 1 has plan 3×2, front elevation 3×1, side elevation 2×1. Views of a cuboid Views of a cuboid View Direction Rectangle / cm Plan From above 3 × 2 Front elevation From front 3 × 1 Side elevation From side 2 × 1
Common Misconceptions to Avoid A square is a rectangle (it has 4 right angles and opposite sides equal) – don't think they are unrelated. A rhombus with equal sides is not necessarily a square unless all angles are 90°. Here, count flat faces separately from curved surfaces. The circular rims of cylinders and cones are curved edges. When counting edges of a pyramid, remember the base edges plus the slant edges. A net must fold without gaps or overlaps; a misplaced flap makes it invalid. Don't confuse plan (top view) with front elevation (front view). Typical Exam Questions Name a shape from its properties (e.g., 'I have 4 equal sides and 4 right angles' → square). State the number of faces, edges, and vertices of a given solid (e.g., a triangular prism). Draw the net of a given solid (e.g., a cuboid). Draw the plan and elevations of a 3D shape built from cubes. Identify which of several nets forms a cube (only 11 of many arrangements work). Use correct notation: mark parallel sides with arrows, equal sides with dashes, and right angles with squares. 슬라이드 Sign up free to view the lesson slides
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연습 문제 무료 미리 보기 — 62개 중 8개 문제. 가입하면 전부 볼 수 있어요. 1. Which of the following is the correct notation for a point?
Easy 2. How many edges does a triangular prism have?
Easy 3. A square is a type of rectangle.
Easy True or false?
4. Which of the following is a regular polygon?
Medium A Equilateral triangleB Non-square rectangleC Non-equilateral isosceles triangleD Non-rectangular parallelogram5. Which of the following are properties of a cube? (select all that apply)
Medium A 6 facesB 8 verticesC 12 edgesD All faces are rectanglesE All faces are squares6. Match each solid to its number of flat faces. Count curved surfaces separately.
Medium Cube Triangular prism Cylinder 7. Arrange the following shapes in order of increasing number of sides: pentagon, triangle, hexagon, quadrilateral.
Medium Triangle Quadrilateral Pentagon Hexagon 8. Match each solid to the correct number of edges.
Easy Cube Triangular prism Square-based pyramid Cylinder 더 많은 문제 9. Which of the following are properties of a cone? (select all that apply)
Medium A It has one circular base.B It has a curved surface.C It has a vertex (apex).D It has two circular faces.E It has a rectangular face.10. A cylinder has exactly two flat faces.
Easy True or false?
11. Which of the following is a correct net for a cube?
Medium A Four squares in a row, with one above and one below the second squareB Six squares in a single straight rowC Six squares in a 2 by 3 rectangleD Five squares arranged as a cross12. A cuboid has dimensions 4 cm by 3 cm by 2 cm. How many faces does it have?
Medium 13. Match each term to its definition.
Medium A corner point where edges meet A line segment where two faces meet A flat surface A flat two-dimensional surface that extends infinitely 14. A solid has one square base and four triangular faces meeting at an apex. What is it called?
Medium A Square-based pyramidB Triangular prismC CuboidD Cone15. Which of the following is the correct net for a cylinder?
Medium A Two circles and a rectangleB One circle and a triangleC Two rectangles and a squareD One circle and a rectangle16. Which of the following are properties of a regular hexagon? (select all that apply)
Medium A All sides are equalB All interior angles are equalC It has 6 lines of symmetryD It has 6 verticesE It has 6 diagonals17. Arrange the following shapes in order of increasing number of vertices.
Medium Triangle Square Pentagon Hexagon 18. A rectangular prism has dimensions 3 cm by 4 cm by 5 cm. Which calculation gives its volume in cm3 ?
Medium A 3 + 4 + 5B 3 × 4 × 5C 2(3×4) + 2(3×5) + 2(4×5)D 2(3+4+5)19. A cylinder has a radius of 3 cm and a height of 5 cm. What is the volume in cm3 ? (Use π = 3.14)
Medium 20. A cone has a base radius of 4 cm and a height of 9 cm. What is the volume in cm3 ? (Use π = 3.14)
Medium A 150.72B 452.16C 50.24D 113.0421. A sphere has a curved surface and no edges.
Easy True or false?
22. A square-based pyramid has 5 faces and 8 edges.
Medium True or false?
23. Which of the following are properties of a triangular prism? (select all that apply)
Medium A It has 5 faces.B It has 9 edges.C It has 6 vertices.D It has a curved surface.24. Match each solid to the correct number of vertices.
Medium Cube Triangular prism Square-based pyramid 25. Arrange these solids in order of increasing number of flat faces: cylinder, tetrahedron, triangular prism and cube.
Medium Tetrahedron Cylinder Triangular prism Cube 26. A point is a location in space with no size.
Easy True or false?
27. Which description explicitly uses the bar symbol for a line segment with endpoints A and B?
Easy A ABB line ABC AB with a line aboveD A-B28. Which of the following are properties of a cuboid? (select all that apply)
Easy A 6 facesB 8 verticesC 12 edgesD All faces are squaresE All faces are rectangles29. Match each polygon to the correct number of sides.
Medium 30. All squares are rectangles.
Easy True or false?
31. A solid has six congruent square faces, twelve edges and eight vertices. What is its most specific name?
Medium A CuboidB CubeC Triangular prismD Square-based pyramid32. Arrange the following solids in order of increasing number of edges: cylinder, triangular prism, cube, square-based pyramid.
Medium cylinder square-based pyramid triangular prism cube 33. Match each term to its correct definition.
Easy Parallel lines Perpendicular lines Right angle Plane Distinct lines in the same plane that never meet Lines that meet at 90° An angle of 90° A flat surface 34. Arrange these polygons in order of increasing number of sides: octagon, triangle, hexagon, quadrilateral.
Easy octagon triangle hexagon quadrilateral 35. Which of the following are properties of a regular pentagon? (select all that apply)
Medium A All sides are equalB All interior angles are equalC It has 5 lines of symmetryD It has 5 verticesE It has 6 sides36. A cylinder has two curved surfaces.
Easy True or false?
37. Which of the following nets will NOT form a cube?
Medium A Four squares in a row, with one above and one below the second squareB Four squares in a row, with one above and one below the third squareC Four squares in a row, with one above the first square and one below the fourthD Six squares arranged as a 2 by 3 rectangle38. Which of the following are properties of a square-based pyramid? (select all that apply)
Medium A It has 5 facesB It has 8 edgesC It has 5 verticesD It has 4 triangular facesE It has a square base39. Arrange these solids in order of increasing number of flat faces: cylinder, tetrahedron, triangular prism and cube.
Medium cylinder triangular prism tetrahedron cube 40. A cuboid has dimensions 5 cm, 4 cm, and 3 cm. What is its volume in cm3 ?
Medium 41. How many vertices does a square-based pyramid have?
Medium 42. Complete the sentence with the correct term.
Easy A line that intersects another line at a right angle is said to be ____ to it.
43. What is the name of the solid that has one circular base and a curved surface meeting at a point?
Easy 44. How many vertices does the cuboid have?
Medium 45. How many edges does the cuboid have?
Medium 46. How many faces does the cuboid have?
Medium 47. A cube has 12 edges. How many edges does a triangular prism have?
Medium 48. Fill in the blanks with the correct terms.
Easy A polygon with all sides equal and all angles equal is called a ____ polygon.
49. Complete the sentence.
Medium Two lines that are always the same distance apart and never meet are called ____ lines.
50. How many edges does a square-based pyramid have?
Medium 51. A cuboid has dimensions 5 cm by 4 cm by 3 cm. How many faces does it have?
Easy 52. A triangular prism has a triangular face with base 6 cm and height 4 cm. If the prism is 10 cm long, what is the volume in cm3 ?
Medium 53. Explain why a square is also a rectangle.
Medium 54. Explain the difference between a plan view and a front elevation of a 3D shape.
Medium 55. How many vertices does a square-based pyramid have?
Medium 56. How many vertices does the cuboid have?
Medium 57. How many edges does the cuboid have?
Medium 58. How many faces does the cuboid have?
Medium 59. A cube has 12 edges. How many edges does a triangular prism have?
Medium A 11 edgesB 9 edgesC 8 edgesD 10 edges60. How many edges does a square-based pyramid have?
Medium A 9 edgesB 10 edgesC 8 edgesD 7 edges61. A cuboid has dimensions 5 cm by 4 cm by 3 cm. How many faces does it have?
Easy 62. A triangular prism has a triangular face with base 6 cm and height 4 cm. If the prism is 10 cm long, what is the volume in cm3 ?
Medium A 108 cm3 B 132 cm3 C 120 cm3 D 144 cm3 Unlock all 62 questions & more 무료 계정을 만들어 이 주제의 모든 문제, 슬라이드, 플래시카드, 복습 노트를 확인하세요.
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