NCERT Solutions for Class 7th Maths Chapter 7 A Tale of Three Intersecting Lines
Updated on 2026-09-08
About this chapter
A triangle has three vertices, three sides and three angles. It is named by its vertices in any order — ∆ABC, ∆BAC and ∆CAB are the same triangle. Two arcs drawn with a compass meet at the third vertex, so a triangle whose three sidelengths are known can be constructed exactly, without trial and error. Triangle inequality: a triangle exists for three lengths exactly when each length is less than the sum of the other two. It is enough to test the longest length. A triangle can also be built from two sides and the included angle , or from two angles and the included side — the latter only when the two angles add to less than 180°. Angle sum property: the three angles of any triangle add up to 180°. The proof draws a line through one vertex parallel to the opposite side. An altitude is the pe
- Constructing a Triangle When its Sides are Given
- Are Triangles Possible for any Lengths?
- Triangle Inequality
- Visualising the construction of circles
- When do the two circles intersect?
- Conclusion
- Two Sides and the Included Angle
- Two Angles and the Included Side
- Do triangles always exist?
- Finding the third angle
Exercises
- Introduction · 7.1 Equilateral Triangles · 7.2 Constructing a Triangle When its Sides are Given — In-text Questions Page 146–149
- Construct — Constructing a Triangle When its Sides are Given Page 150
- Figure it Out — Constructing a Triangle When its Sides are Given Page 150–151
- Are Triangles Possible for any Lengths? — In-text Questions Page 151
- Triangle Inequality — In-text Questions Page 152–153
- Triangle Inequality — Figure it Out Page 154
- Triangle Inequality — In-text Questions Page 154
- Visualising the construction of circles — In-text Questions Page 155
- Triangle Inequality — Figure it Out Page 156
- When do the two circles intersect? — In-text Questions Page 156–159
- Conclusion — Figure it Out Page 159–160
- .3 Construction of Triangles When Some Sides and Angles are Given — In-text Questions Page 1607
- Two Sides and the Included Angle — Figure it Out Page 161
- Two Angles and the Included Side — In-text Questions Page 161
- Two Angles and the Included Side — Figure it Out Page 162
- Do triangles always exist? — In-text Questions Page 162–163
- Do triangles always exist? — Figure it Out Page 163
- Finding the third angle — In-text Questions Page 164
- Finding the third angle — Figure it Out Page 165
- Angle Sum Property · Exterior Angles — In-text Questions Page 165–167
- .4 Constructions Related to Altitudes of Triangles — In-text Questions Page 167–1697
- .5 Types of Triangles — In-text Questions Page 1707
- .5 Types of Triangles — Figure it Out Page 170–1717
- Shortest Path in a Box! — Puzzle Time Page 172