Key Concepts
- Lines
- Classification of Triangles
- Classification of Quadrilaterals
Lines
Introduction:
Definition
Line:
A line is a figure formed when two points are connected with minimum distance between them and have no ends on both sides.
![Line](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5700.png)
A line AB is represented by
AB↔
A real-life example of a line
![Fig 4 (Roadway lines)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5703.png)
Line Segment:
A line segment is part of a line that has a fixed endpoint on both the ends.
![Line Segment:](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5702.png)
A line segment AB is represented by AB−
A real-life example of a line segment
![Fig 6 (Soccer ground)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5728.png)
Ray:
A ray is a part of a line that has only one fixed point, and the other point does not have any end.
![Ray:](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5704.png)
A line segment AB is represented by AB→
A real-life example of a ray
![Fig 8 (Torchlight rays and beams)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5729.png)
Types of lines:
Basically, lines are of 3 types:
- Parallel lines
- Intersecting lines
- Perpendicular lines
- Parallel lines
Two lines are said to be parallel lines if they lie in the same plane and never meet.
Parallel lines
![Parallel lines](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5730.png)
Non- Parallel lines
![Non- Parallel lines](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5731.png)
A real-life example of parallel lines
![Fig 10 (Railway tracks)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5706.png)
- Intersecting lines
If two lines meet at a point, they are said to be intersecting lines.
![Fig 11 (Intersecting lines)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5705-1024x534.png)
A real-life example of intersecting lines
![Fig 12 (Scissor)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5707.png)
Scissors, the two blades of the scissors intersect at each other to make it work effectively.
- Perpendicular lines
When two lines intersect at an angle of 90o or at a right angle, then they are perpendicular to each other.
![Fig 13 (Perpendicular lines)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5732.png)
![Fig 14 (Non Perpendicular lines)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5708.png)
A real-life example of perpendicular lines
![Fig 14 (Clock)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5709.png)
Clocks are the best examples to show perpendicular lines at 3 O’ clock and 9 O’ clock.
Classification of Triangles
Triangle (Definition)
A triangle is a closed shape with three angles, three sides and three vertices.
![Triangle (Definition)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5710-1024x712.png)
Triangles can be classified as:
- On the basis of angles
- On the basis of measurement of their sides
![Fig 16 (Types of triangles)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5733.png)
A real-life example of triangles
![Fig 17 (Sailing boat)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5734.png)
Classification of Quadrilaterals
Quadrilateral
A quadrilateral is a closed two-dimensional shape that has 4 sides, 4 angles, and 4 vertices.
![Quadrilateral](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5711.png)
A real-life example of a quadrilateral
![Fig 19 (Boxer fight Cancun box quadrilateral)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5712.png)
Types of Quadrilaterals:
Quadrilaterals are classified based on their sides, angles, and diagonals.
![Types of Quadrilaterals:](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5713-749x1024.png)
A real-life example of types of quadrilaterals
![chess](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5714.png)
![house](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5715.png)
![sign board](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-238.jpeg)
![paltter](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5716.png)
Exercise:
- Find out the number of sleeping lines, slanting lines, curved lines, circles, square, triangle and rectangle in the figure below:
![exercise](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5735.png)
- Is it possible to have an obtuse acute triangle? Explain.
- What is true about all quadrilaterals?
- What is the difference between a square, and a rhombus?
- Can a trapezoid have perpendicular sides?
- Classify each triangle by its sides, and then by its angles.
- The blades of an open pair of scissors look like what pair of lines?
- What geometric term could you use to describe the top, and bottom edges of a book?
- How many acute angles are there in an equilateral triangle?
- What kinds of triangles never have right angles?
What we have learnt:
- Recognize and define lines, line segments and rays
- Understand parallel and perpendicular lines
- Understand triangles based on angles
- Understand triangles based on sides
- Learn quadrilaterals and classification of quadrilaterals
- Solve questions based on lines, angles, and shapes
Concept Map:
Classification of Lines
![lines](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/lines.png)
![All About Lines](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5736.png)
Classification of Quadrilaterals
![Classification of Quadrilaterals](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5726-1024x527.png)
Classification of Triangles
![Classification of Triangles](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5727-1024x498.png)
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