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Geometric Twins

When shape is not enough

Hold up a small bangle and a big one. The shape is the same. Neither fits the other wrist.

Look at each pair. Choose its name.

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All three corners agree. Every side differs.

Corners give the shape, not the size

AAA (angle, angle, angle) is not a test for congruence. Three equal angles give the same shape. They do not tell the size.

Example: two triangles with corners 40°, 60° and 80°. The corners add to 180°: 40 + 60 + 80 = 180. One is small. One is large. They are not congruent.

Sides in one ratio: every side is multiplied by the same number.

Two figures, three answers
What matchesWhat you can say
Every side and every cornerCongruent
Every corner, sides in one ratioSame shape, new size
NeitherNot even the same shape

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This track

  1. 0 Start here
  2. 1 Landing one on the other
  3. 2 Slide it, turn it, flip it
  4. 3 A bigger copy is a different figure
  5. 4 One line, one corner
  6. 5 Three sides settle it
  7. 6 Two sides and the corner between them
  8. 7 Two corners and a side
  9. 8 When shape is not enough
  10. 9 Writing a congruence in order
  11. 10 RHS: a right angle, the hypotenuse, a side
  12. 11 Equal sides, equal angles
  13. 12 Twins hiding in a figure
  14. 13 Checkpoint: order, RHS and angles
  15. 14 The big picture
  16. 15 Track quiz

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