★
Unit review: symmetry and solid shapes
Textbook: Part 4, unit review, pp. 58–59
GoalReview of symmetry and solids: axes of symmetry, symmetric points, prisms, pyramids, cylinders, cones and their nets.
New words
axis of symmetry · simmetriya o‘qinet · yoyilmaprism · prizmapyramid · piramida
Explanation
In this unit we learned line symmetry, reflection and point symmetry, finding the area of irregular shapes, the cuboid, prism, pyramid, sphere, cylinder and cone, and their nets. A prism with an n-sided base has n + 2 faces, 3n edges and 2n vertices; a pyramid has n + 1 faces, 2n edges and n + 1 vertices.
Worked examples
The point symmetric to A(2; 3) across the vertical axis x = 5 is (8; 3).
A cylinder's lateral net is a 25 cm × 8 cm rectangle: 25 × 8 = 200 cm².
Class activity
“Solids market”: children match cards of solids (cube, prism, pyramid, cylinder, cone, sphere) with names, numbers of faces/edges/vertices and nets.
Practice
1
How many axes of symmetry does a square have?
4
2
Write the coordinates of the point symmetric to A(2; 3) across the vertical axis x = 5.
(8; 3)
3
How many faces does a pentagonal prism have?
7
4
How many edges does a pyramid with a hexagonal base have?
12
5
The lateral net of a cylinder is a 25 cm × 8 cm rectangle. What is its area in cm²?
200