maths
properties of quadrilateral
The first sketch is a square. A square has 4 equal sides and 4 right angles. Two pairs of parallel sides
The second sketch is a rectangle. A rectangle has two pairs of equal sides and four right angles. Two pairs of parallel sides
The third sketch is a rhombus. A rhombus has 4 equal sides and opposite angles are equal. Two pairs of parallel sides
The fourth sketch is a parallelogram. A parallelogram has two pairs of parallel sides and opposite sides are equal. Opposite angles are equal
The fifth sketch is a trapezoid. A trapezoid has only one pair of parallel sides
The sixth sketch is a kite. A kite has two pairs of adjacent sides that are equal. No parallel sides
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congruence means the same ............ shape in a different......................
Congruence means the same size and shape in a different position (or orientation)
The properties of each 3D shape
Answer: The properties of each 3D shape are listed above. Note that shape 7 is a 2D shape and does not fit the criteria of the other shapes.<hide>Diagram description: The diagram shows nine 3D shapes. Shape 1 is a cuboid, shape 2 is a triangular prism, shape 3 is a cone, shape 4 is a square-based pyramid, shape 5 is a cylinder, shape 6 is a cube, shape 7 is a circle (2D), shape 8 is a square-based pyramid viewed from above, and shape 9 is a pentagonal prism.</hide>
Step 1: Identify the name and properties of each 3D shape.
Shape 1: Cuboid. Vertices: 8, Faces: 6, Edges: 12
Shape 2: Triangular Prism. Vertices: 6, Faces: 5, Edges: 9
Shape 3: Cone. Vertices: 1, Faces: 2, Edges: 1
Shape 4: Square-based Pyramid. Vertices: 5, Faces: 5, Edges: 8
Shape 5: Cylinder. Vertices: 0, Faces: 3, Edges: 2
Shape 6: Cube. Vertices: 8, Faces: 6, Edges: 12
Shape 7: Circle (2D shape, not a 3D shape). Vertices: 0, Faces: 1, Edges: 0
Shape 8: Square-based Pyramid (top view). Vertices: 4, Faces: 4, Edges: 4
Shape 9: Pentagonal Prism. Vertices: 10, Faces: 7, Edges: 15
what is a face
A face, in the context of 3D shapes, is a flat surface that forms part of the boundary of the solid shape. Think of it as one of the sides of a box (cuboid) or one of the triangular sides of a pyramid. Each face is a polygon (a closed two-dimensional shape with straight sides)
what is an edge
In 3D shapes, an edge is the line segment where two faces meet. It's the straight line you see where two flat surfaces connect. Think of the corners of a box; each corner line is an edge.
what is a plan view
A plan view is a top-down view of a 3D object. Imagine looking directly down on the object from above; the image you see is the plan view. It shows the shape as it would appear projected onto a horizontal plane. In the case of the square-based pyramid (Shape 8 in your diagram), the plan view would simply show the square base.
a net is a ......... version of a 3D shape
A net is a two-dimensional version of a 3D shape.
what is a vertices
Vertices (the singular is vertex) are the points where edges of a 3D shape meet. They are the corners or points of the shape. Think of the corners of a cube –
division ➗️ faction
3.9 ÷3
Method 3: Breaking it down
Think of 3.9 as 3 + 0.9.
Divide 3 by 3: 3 ÷ 3 = 1
Divide 0.9 by 3: 0.9 ÷ 3 = 0.3
Add the results: 1 + 0.3 = 1.3
All three methods give you the same answer: 1.3
The properties of each 3D shape
Answer: The properties of each 3D shape are listed above. Note that shape 7 is a 2D shape and does not fit the criteria of the other shapes.<hide>Diagram description: The diagram shows nine 3D shapes. Shape 1 is a cuboid, shape 2 is a triangular prism, shape 3 is a cone, shape 4 is a square-based pyramid, shape 5 is a cylinder, shape 6 is a cube, shape 7 is a circle (2D), shape 8 is a square-based pyramid viewed from above, and shape 9 is a pentagonal prism.</hide>
Step 1: Identify the name and properties of each 3D shape.
Shape 1: Cuboid. Vertices: 8, Faces: 6, Edges: 12
Shape 2: Triangular Prism. Vertices: 6, Faces: 5, Edges: 9
Shape 3: Cone. Vertices: 1, Faces: 2, Edges: 1
Shape 4: Square-based Pyramid. Vertices: 5, Faces: 5, Edges: 8
Shape 5: Cylinder. Vertices: 0, Faces: 3, Edges: 2
Shape 6: Cube. Vertices: 8, Faces: 6, Edges: 12
Shape 7: Circle (2D shape, not a 3D shape). Vertices: 0, Faces: 1, Edges: 0
Shape 8: Square-based Pyramid (top view). Vertices: 4, Faces: 4, Edges: 4
Shape 9: Pentagonal Prism. Vertices: 10, Faces: 7, Edges: 15
properties of quadrilateral
Answer: The table should be filled as follows:
| Sketch | Name | Sides | Parallel Sides | Angles |
|---|---|---|---|---|
| [Square] | Square | 4 equal sides | 2 pairs | 4 right angles |
| [Rectangle] | Rectangle | 2 pairs of equal sides | 2 pairs | 4 right angles |
| [Rhombus] | Rhombus | 4 equal sides | 2 pairs | Opposite angles equal |
| [Parallelogram] | Parallelogram | 2 pairs of equal sides | 2 pairs | Opposite angles equal |
| [Trapezoid] | Trapezoid | | 1 pair | |
| [Kite] | Kite | 2 pairs of adjacent equal sides | | |
Step 1: The first figure is a square. It has 4 equal sides and 4 right angles. Both pairs of opposite sides are parallel.
Step 2: The second figure is a rectangle. It has 2 pairs of equal sides and 4 right angles. Both pairs of opposite sides are parallel.
Step 3: The third figure is a rhombus. It has 4 equal sides and opposite angles are equal. Both pairs of opposite sides are parallel.
Step 4: The fourth figure is a parallelogram. It has 2 pairs of equal and parallel sides. Opposite angles are equal.
Step 5: The fifth figure is a trapezoid. It has only one pair of parallel sides.
Step 6: The sixth figure is a kite. It has two pairs of adjacent sides that are equal in length.
Isosceles Trapezoid
Answer: The table above shows the properties of the quadrilaterals.<hide>The image contains a table to classify quadrilaterals based on their properties. The table has columns for a sketch of the quadrilateral, its name, the number of sides, the number of parallel sides, and the angles. The task is to fill in the table with the correct information for each quadrilateral.</hide>
Step 1: Identify the quadrilaterals.
The sketches represent a square, a rectangle, a rhombus, a parallelogram, a trapezoid, an isosceles trapezoid, and a kite.
Step 2: Fill in the table.
| Sketch | Name | Sides | Parallel Sides | Angles |
|---------|-----------------|-------|-----------------|---------------------------------------|
| □ | Square | 4 | 2 | 4 right angles (90°) |
| □ | Rectangle | 4 | 2 | 4 right angles (90°) |
| ◊ | Rhombus | 4 | 2 | Opposite angles are equal |
| ▱ | Parallelogram | 4 | 2 | Opposite angles are equal |
| 梯 | Trapezoid | 4 | 1 | No specific angle relationship |
| 梯 | Isosceles Trapezoid | 4 | 1 | Base angles are equal |
| 凧 | Kite | 4 | 0 | Two pairs of adjacent angles are equal |