Master Chapter 7 Class 7 - A tale of three Intersecting Lines (Ganit Prakash) with comprehensive NCERT Solutions, Practice Questions, MCQs, Sample Papers, Case Based Questions, and Video lessons.
Start Learning NowWelcome to Chapter 7, A Tale of Three Intersecting Lines, from your Class 7 Maths book, Ganita Prakash.
What happens when you draw three straight lines on a page so that they all intersect? You get a triangle—the most basic and one of the most important closed shapes in all of geometry. A triangle is a simple figure, but it is incredibly strong and full of fascinating rules and properties.
This chapter is a deep dive into the world of triangles. You will learn how to build them from scratch with precision and discover the logical rules that govern their sides and angles.
This chapter is a hands-on guide to both constructing triangles and understanding their fundamental properties.
Constructing Triangles: We will move beyond freehand sketching and learn the formal geometric methods for drawing triangles using a ruler and compass. You will learn how to build a perfect triangle given specific pieces of information:
SSS (Side-Side-Side): How to construct a triangle when you know the lengths of all three sides.
SAS (Side-Angle-Side): How to construct a triangle when you know two sides and the angle between them.
ASA (Angle-Side-Angle): How to construct a triangle when you know two angles and the side between them.
The Triangle Inequality Rule: A key question we will answer is: can you make a triangle out of any three side lengths? You will discover a fundamental rule of nature called the Triangle Inequality. This rule states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. We'll explore why this is true and how to use it to instantly tell if a triangle is possible or not.
The Angle Sum Property: You will learn one of the most famous and useful properties in geometry: the three angles inside any triangle—no matter its shape or size—always add up to $180^\circ$. We will even explore the logical proof for why this is always true.
Altitudes and Types of Triangles: We will also explore special lines and classifications:
Altitudes: You will learn what an altitude (or height) of a triangle is and how to construct one.
Classifying Triangles: We will review the types of triangles based on their sides (equilateral, isosceles, scalene) and their angles (acute, right, obtuse).
This chapter is your foundation for geometry. Mastering these construction skills and understanding the core properties of triangles will give you the power to solve all kinds of geometric problems. At Teachoo, we will guide you through every single construction, step-by-step, and break down each property so you can understand it perfectly.
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