CBSE · Class 7 · Mathematics · Chapter 7

A Tale of Three Intersecting Lines

Investigate triangles, their properties and geometric constructions using three intersecting lines.

10 lessons 50 min
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Lessons in this chapter

  1. 1Equilateral TrianglesSee how two compass arcs locate the third vertex of a triangle with three equal sides.
  2. 2Constructing a Triangle When its Sides are GivenUse two distance constraints to construct a triangle from three side lengths.
  3. 3Are Triangles Possible for any Lengths?Discover why the three lengths must satisfy a shortest-path relationship before a triangle can exist.
  4. 4Triangle InequalityExplain exactly when three lengths make a triangle and how to find the possible third side.
  5. 5Two Sides and the Included AngleConstruct a triangle by fixing the angle between two given sides.
  6. 6Two Angles and the Included SideConstruct from a side and its endpoint angles, then discover when the two rays meet.
  7. 7Angle Sum Property and Exterior AnglesUse a parallel line to explain the 180° angle sum and the exterior-angle relationship.
  8. 8Constructions Related to Altitudes of TrianglesUnderstand perpendicular height and construct altitudes inside, outside, and along a triangle’s sides.
  9. 9Types of TrianglesClassify triangles by their sides and angles, then explore how the two descriptions can be combined.
  10. 10Chapter Summary and PracticeConnect triangle constructions, existence rules, angle relationships, altitudes, and classification through mixed revision.
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