Coordinates, polygons and shape properties
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课程笔记
The Coordinate Plane
- A coordinate plane is a flat surface with two number lines that cross at a right angle.
- The x-axis is the horizontal (left-right) number line.
- The y-axis is the vertical (up-down) number line.
- The origin is the point where the two axes meet. Its coordinates are (0, 0).
- Each point on the plane is named by an ordered pair like (3, 5). The first number is the x-coordinate (how far right), the second is the y-coordinate (how far up).
- We only use the first quadrant in Grade 5, so all coordinates are positive (or zero).
Plotting and Reading Points
- To plot a point, start at the origin. Move right along the x-axis by the first number, then move up by the second number.
- For example, (4, 2) means move 4 steps right and 2 steps up.
- To read a point, look at where it is. The x-coordinate is how far right from the origin, and the y-coordinate is how far up.
- Always write coordinates in brackets with a comma: (x, y).
- Points on the x-axis have y = 0, like (3, 0). Points on the y-axis have x = 0, like (0, 5).
Using Coordinates in Problems
- You can use coordinates to describe where things are on a map or grid.
- For example, a treasure at (2, 3) is 2 steps right and 3 steps up from the origin.
- To find the distance between two points on the same horizontal line, subtract the x-coordinates.
- To find the distance between two points on the same vertical line, subtract the y-coordinates.
- Always check that your answer makes sense by looking at the grid.
Polygons and Their Sides
- A polygon is a flat shape with straight sides that close up.
- Polygons are named by the number of sides they have.
- A triangle has 3 sides.
- A quadrilateral has 4 sides.
- A pentagon has 5 sides.
- A hexagon has 6 sides.
- An octagon has 8 sides.
Classifying Triangles
- Triangles can be classified by their sides.
- An equilateral triangle has all three sides equal.
- An isosceles triangle has two sides equal.
- A scalene triangle has no sides equal.
- Triangles can also be classified by their angles: acute (all angles less than 90°), right (one angle exactly 90°), and obtuse (one angle more than 90°).
- The sum of the angles in any triangle is always 180°.
Classifying Quadrilaterals
- A quadrilateral is any 4-sided polygon.
- A rectangle has four right angles and opposite sides equal.
- A square has four equal sides and four right angles.
- A rhombus has four equal sides but not necessarily right angles.
- A parallelogram has opposite sides parallel and equal.
- A trapezoid has at least one pair of parallel sides.
- A square is also a rectangle and a rhombus because it has all their properties.
Shape Properties and Missing Values
- Use the properties of a shape to find missing angles or sides.
- In a triangle, if you know two angles, subtract their sum from 180° to find the third.
- In a rectangle, opposite sides are equal, so if one side is 5 cm, the opposite side is also 5 cm.
- In a square, all sides are equal, so if one side is 3 cm, all sides are 3 cm.
- In a parallelogram, opposite angles are equal, and adjacent angles add up to 180°.
Transformations: Reflection and Translation
- A translation slides a shape without turning or flipping it.
- When you translate a shape, every point moves the same distance and direction.
- A reflection flips a shape over a line, like a mirror.
- The line you flip over is called the line of reflection.
- After a reflection, the shape is the same size and shape, but it is reversed.
- You can use a grid to help you move or flip shapes accurately.
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练习题
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1.What is the name of the point where the x-axis and y-axis meet?
Easy- AOrigin
- BVertex
- CCenter
- DIntersection
2.In the ordered pair (3, 5), which number is the x-coordinate?
Easy- A3
- B5
- CBoth
- DNeither
3.The point (0, 0) is called the origin.
EasyTrue or false?
4.Which point is located at (2, 4) on a coordinate grid?
Easy- A2 units right and 4 units up
- B4 units right and 2 units up
- C2 units left and 4 units up
- D4 units left and 2 units up
5.Which of the following are polygons? (Select all that apply)
Medium- ATriangle
- BCircle
- CSquare
- DRectangle
- EPentagon
6.Match each polygon with its number of sides.
Easy- Triangle
- Quadrilateral
- Pentagon
- 3 sides
- 4 sides
- 5 sides
7.Order these shapes from fewest sides to most sides.
Medium- Triangle
- Square
- Pentagon
- Hexagon
8.Every square is also a rectangle.
MediumTrue or false?
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