Symmetry and solid shapes: Class 7 maths video

0:00 Class 7 maths. Symmetry and solid shapes.

0:04 Welcome aboard, superhero cadet!

0:07 Captain Calc needs your help to inspect superhero logos and 3D space bases for perfect symmetry.

0:15 Line Symmetry in 2D Shapes.

0:18 A line of symmetry divides a shape into two identical mirror halves.

0:23 When folded along a line of symmetry, both halves overlap completely.

0:28 Try this one. How many lines of symmetry does a regular pentagon have?

0:34 A regular pentagon has 5 equal sides and 5 equal interior angles.

0:41 For any regular polygon, the number of lines of symmetry equals the number of sides.

0:47 Therefore, a regular pentagon has 5 lines of symmetry.

0:51 So the answer is 5.

0:53 Rotational Symmetry.

0:55 A shape has rotational symmetry if it looks identical to its original position after a turn of less than 360°.

1:05 The order of rotational symmetry is the number of times the shape matches itself during a full 360° turn.

1:15 Try this one. What is the order of rotational symmetry of a square?

1:21 Rotate a square by 90°, 180°, 270°, and 360°.

1:31 It fits onto its original shape 4 times during one complete turn.

1:36 Therefore, the order of rotational symmetry is 4.

1:40 So the answer is 4.

1:42 3D Solid Shapes and Their Components.

1:46 Three-dimensional solid shapes have length, width, and height.

1:50 Flat surfaces are called faces, straight lines where faces meet are edges, and corner points are vertices.

1:59 Try this one. Find the number of faces, vertices, and edges of a triangular prism.

2:07 A triangular prism has 2 triangular bases and 3 rectangular side faces. Total faces F = 2 + 3 = 5.

2:17 It has 3 top vertices and 3 bottom vertices. Total vertices V = 6.

2:24 It has 3 top edges, 3 bottom edges, and 3 vertical side edges. Total edges E = 9.

2:31 So the answer is F=5, V=6, E=9.

2:37 Euler's Formula for Polyhedrons.

2:40 Euler's formula states that for any 3D polyhedron, F + V - E = 2.

2:47 F stands for the number of flat faces, V for vertices, and E for edges.

2:52 Try this one. A polyhedron has 8 faces and 12 vertices. Calculate its number of edges.

3:01 Write Euler's formula: F + V - E = 2.

3:05 Substitute the given values: 8 + 12 - E = 2.

3:10 Simplify to get 20 - E = 2, which gives E = 20 - 2 = 18.

3:18 So the answer is 18.

3:20 Your turn. How many lines of symmetry does a regular hexagon have? Pause the video, and try it.

3:29 The answer is 6.

3:32 Well done! Now try the practice and the quiz in this lesson on LearnFun.