CBSE · Class 7 · Mathematics · Chapter 9

Geometric Twins

Understand congruent figures and investigate the conditions that guarantee congruence of triangles.

10 lessons 50 min
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Lessons in this chapter

  1. 1Geometric TwinsLearn what makes two figures exact copies and which measurements can recreate them.
  2. 2Measuring the SidelengthsConstruct a triangle from three side lengths and see why its reflected copy is congruent.
  3. 3Conventions to Express CongruenceMatch vertices in order so every side and angle comparison means the right thing.
  4. 4Measuring Two Sides and the Included AngleDiscover why an angle between two measured sides fixes a triangle, while three angles alone do not.
  5. 5Measuring Two Sides and a Non-included AngleSee how the same two side lengths and a non-included angle can produce two different triangles.
  6. 6Two Angles and a SideUse two angles and one length to fix a triangle, and connect angle facts with congruence proofs.
  7. 7Measuring Two Sides in a Right TriangleIdentify the hypotenuse and use the right angle, hypotenuse, and one side to establish congruence.
  8. 8Using Congruence to Prove Equal PartsBuild clear geometry proofs from given facts, a sufficient condition, and the correct matching of parts.
  9. 9Angles of Isosceles and Equilateral TrianglesDerive equal base angles from RHS and use them in triangle calculations and familiar patterns.
  10. 10Chapter Summary and PracticeConnect all five congruence conditions, revisit angle properties, and solve mixed proofs and visual challenges.
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