A Tale of Three Intersecting Lines — Class 7 Mathematics
Ganita Prakash Part 1 · Chapter 7
CBSE Class 7 community
View allMathematics
2~140days leftAnnual exams · school dates varyFeb–Mar 2027 · school-specific · tentative
All 2 books, one purchase- Mathematics
All available subjects
7~140days leftAnnual exams · school dates varyFeb–Mar 2027 · school-specific · tentative
Every subject, one purchase- Mathematics
- Science
- + 3 more
Social Science
~140days leftAnnual exams · school dates varyFeb–Mar 2027 · school-specific · tentative
All 2 books, one purchase- Social Science
हिंदी
~140days leftAnnual exams · school dates varyFeb–Mar 2027 · school-specific · tentative
Every important point, highly compressed.- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
Science
~140days leftAnnual exams · school dates varyFeb–Mar 2027 · school-specific · tentative
Every important point, highly compressed.- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
English · Poorvi
~140days leftAnnual exams · school dates varyFeb–Mar 2027 · school-specific · tentative
Every important point, highly compressed.- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
Chapter summary
This chapter is about triangles — their construction, existence and angle properties. Using a compass and ruler you construct equilateral triangles (all sides equal), isosceles triangles (two sides equal) and scalene triangles (all sides different) by drawing arcs from the endpoints of a base. A central idea is the triangle inequality: a triangle exists only when each side is shorter than the sum of the other two. So lengths like 10, 15, 30 cannot form a triangle because
Constructing equilateral, isosceles and scalene trianglesTriangle inequality and existence of trianglesConstructing triangles from sides and anglesAngle sum property and exterior anglesAltitudes and classifying triangles
Key ideas & terms
- Equilateral triangle
- A triangle with all three sides equal (and all angles
). - Isosceles triangle
- A triangle with exactly two sides equal.
- Scalene triangle
- A triangle with all three sides of different lengths.
- Triangle inequality
- Each side of a triangle is shorter than the sum of the other two sides.
- Angle sum property
- The three angles of any triangle add up to
. - Exterior angle
- The angle between a side of a triangle extended and the adjacent side.
- Altitude
- A perpendicular line segment from a vertex to the opposite side (or its extension).
Extra questions & answers
State the triangle inequality.
Each side of a triangle must be less than the sum of the other two sides.
Can 10, 15 and 30 be the sides of a triangle?
No, because
Can 4, 5 and 8 form a triangle?
Yes, because
What is the angle sum property of a triangle?
The three interior angles add up to
If two angles of a triangle are 36° and 72°, find the third.
The third angle is
What is an equilateral triangle?
A triangle with all three sides equal and all angles
What is an isosceles triangle?
A triangle with exactly two sides of equal length.
What is an altitude of a triangle?
A perpendicular segment from a vertex to its opposite side.
When can two given angles form a triangle?
When their sum is less than
What is an exterior angle of a triangle?
The angle between an extended side and the adjacent side;