பீட்டாஇந்த தளம் தீவிர வளர்ச்சியில் உள்ளது; பிழைகள், விடுபட்ட அம்சங்கள் மற்றும் தரவு இழப்பு அபாயம் உள்ளன. உங்கள் ஆதரவுக்கு நன்றி!

Symmetry And Shapes

விளையாடிக் கற்றுக்கொள்ளுங்கள்

ஆற்றல் சம்பாதிக்க இந்த கேள்விகளுக்குப் பதிலளியுங்கள், பின்னர் மீன் பிடித்து ஆராயுங்கள். கணக்கு தேவையில்லை.

ஆசிரியர்களுக்கு: Symmetry And Shapes (Maths [CIE], Core)-க்கான தயாரான பாட ஸ்லைடுகள், திருப்புதல் குறிப்புகள், வரைபடங்கள் — உங்கள் பாடத்தில் அவற்றைப் பயன்படுத்தவும், அல்லது மாணவர்கள் நேரலை விளையாட்டாக விளையாடும் ஊடாடும் வகுப்பு செயல்பாடாக தலைப்பை இயக்கவும்.

பாட குறிப்புகள்

Introduction to Lines & Angles

  • A line is straight, one-dimensional, and extends forever; a line segment has a start and end point.
  • Parallel lines never intersect and are marked with arrows; perpendicular lines intersect at right angles (90°).
  • Acute angle: less than 90°; right angle: exactly 90°; obtuse angle: greater than 90° but less than 180°.
  • Straight angle: exactly 180°; reflex angle: greater than 180° but less than 360°.
  • Angles at a point sum to 360°; angles on a straight line sum to 180°; angles that sum to 180° are supplementary.

Types of angles

Types of angles

Rotational Symmetry

  • Rotational symmetry is the number of times a shape looks the same during a full 360° rotation; this number is the order of rotational symmetry.
  • Use tracing paper with an arrow to track orientation; returning to the start counts as 1, so order is at least 1.
  • A shape with order 1 has no rotational symmetry (only looks the same at the start).
  • A regular octagon has rotational symmetry of order 8; a regular pentagon has order 5.

Finding rotational symmetry with tracing paper

Finding rotational symmetry with tracing paper

Lines of Symmetry

  • A line of symmetry divides a shape into two mirror-image halves; folding along it makes the halves coincide.
  • Some shapes have multiple lines of symmetry (e.g., square has 4, rectangle has 2).
  • To complete a shape given a line of symmetry, reflect the given part across the line.
  • Diagonal lines of symmetry require careful reflection; tracing paper can help.

Lines of symmetry

Lines of symmetry

Properties of Polygons

  • Polygons are named by number of sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), nonagon (9), decagon (10).
  • A regular polygon has all sides equal and all angles equal.
  • Triangles: equilateral (3 equal sides/angles), isosceles (2 equal sides/angles), right-angled (one 90° angle), scalene (no equal sides).
  • Quadrilaterals: square (4 equal sides, 4 right angles, 4 lines of symmetry, order 4 rotational symmetry).
  • Rectangle: opposite sides equal, 4 right angles, 2 lines of symmetry, order 2 rotational symmetry.
  • Parallelogram: opposite sides parallel and equal, opposite angles equal, no lines of symmetry, order 2 rotational symmetry.
  • Rhombus: all sides equal, opposite sides parallel, opposite angles equal, 2 lines of symmetry, order 2 rotational symmetry.
  • Trapezium: one pair of parallel sides; isosceles trapezium: non-parallel sides equal, 1 line of symmetry.
  • Kite: two pairs of equal adjacent sides, one pair of equal opposite angles, 1 line of symmetry, order 1 rotational symmetry.

Named polygons

Named polygons

Properties of Circles

  • Key terms: circumference (perimeter), diameter (line through centre, 2× radius), radius (centre to circumference).
  • Chord: line joining two points on circumference; arc: part of circumference; sector: region between two radii and an arc.
  • Segment: region between a chord and an arc; tangent: line touching circle at one point only.
  • Diameter = 2 × radius; ratio circumference/diameter = π.

Parts of a circle

Parts of a circle

Properties of 3D Shapes

  • A prism has the same cross-section throughout; examples: cube (square cross-section), cuboid (rectangle), triangular prism, cylinder (circle).
  • A pyramid has a flat base and sloping sides meeting at an apex; square-based pyramid, tetrahedron (triangular-based pyramid), cone (circular base).
  • Faces: flat surfaces; vertices: corners; edges: lines where faces meet.
  • Cube: 6 square faces, 12 edges, 8 vertices. Cuboid: 6 rectangular faces, 12 edges, 8 vertices.
  • Triangular prism: 2 triangular + 3 rectangular faces, 9 edges, 6 vertices. Square-based pyramid: 1 square + 4 triangular faces, 8 edges, 5 vertices.
  • Cylinder: 2 circular + 1 curved face, 2 edges, 0 vertices. Sphere: 1 curved face, 0 edges, 0 vertices.

Properties of common 3D shapes

Properties of common 3D shapes

Nets of Solids

  • A net is a 2D shape that can be folded to form a 3D solid; the area of the net equals the surface area of the solid.
  • Net of a cube: 6 squares; there are 11 possible nets, the most common is a cross shape.
  • Net of a cuboid: 6 rectangles in three pairs (opposite faces equal); 54 possible nets.
  • Net of a cylinder: two circles (top and bottom) and a rectangle (curved surface); rectangle length = circumference of circle.
  • Net of a square-based pyramid: one square and four congruent triangles.

Nets of common solids

Nets of common solids

ஸ்லைடுகள்

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பதிவு செய்க — இலவசம்உள்நுழைக

பயிற்சி கேள்விகள்

இலவச முன்னோட்டம் — 46-இல் 8 கேள்விகள். அனைத்தையும் பார்க்க பதிவு செய்யவும்.

  1. 1.What is the order of rotational symmetry of a regular octagon?

    Easy
    Regular octagon3 cm
    • A8
    • B4
    • C6
    • D2

  2. 2.What is the mathematical name for a quadrilateral with exactly one pair of parallel sides?

    Easy
    • ATrapezium
    • BParallelogram
    • CRhombus
    • DKite

  3. 3.Write down the mathematical name for an angle which is less than 90°.

    Easy
    • AAcute angle
    • BObtuse angle
    • CRight angle
    • DReflex angle

  4. 4.How many lines of symmetry does a regular pentagon have?

    Easy
    Regular pentagon3 cm
    • A5
    • B4
    • C3
    • D2

  5. 5.What is the order of rotational symmetry of a regular pentagon?

    Easy
    • A5
    • B4
    • C3
    • D2

  6. 6.Write down the mathematical name for a polygon with 5 sides.

    Easy
    • APentagon
    • BHexagon
    • CHeptagon
    • DOctagon

  7. 7.A quadrilateral has rotational symmetry of order 2, exactly two lines of symmetry, and all four sides of equal length. What is its mathematical name?

    Medium
    • ARectangle
    • BRhombus
    • CSquare
    • DParallelogram

  8. 8.A line segment joining two points on the circumference of a circle, but not passing through the centre, is called a

    Easy
    • AChord
    • BDiameter
    • CRadius
    • DTangent

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இந்த தலைப்பிற்கான ஒவ்வொரு கேள்வியையும், ஸ்லைடுகளையும், ஃப்ளாஷ் கார்டுகளையும் மற்றும் திருப்புதல் குறிப்புகளையும் பார்க்க இலவச கணக்கை உருவாக்கவும்.

பதிவு செய்க — இலவசம்உள்நுழைக

முந்தைய தேர்வுகள்

இந்த தலைப்பிற்கான முந்தைய தேர்வு பயிற்சி விரைவில் வருகிறது.
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