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Geometric Twins

Landing one on the other

Slide one tiffin lid onto the other. No gap anywhere. You may slide, turn or flip the copy. A copy that fits exactly on top has landed on it.

Drag the slider. Watch the copy move onto the grey shape.

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A copy sits apart from the grey target.
Step 1 of 4
  1. A copy sits apart from the grey target.
  2. Slide it, and turn it, toward the target.
  3. It lands exactly on the target. No gaps.
  4. Every side now carries a matching tick mark.

The test for twins

Two figures are congruent when one lands exactly on the other. They have the same shape and the same size.

Every corner sits on a corner. Every side sits on a side.

Three questions about two figures
QuestionWhat it tells you
Do they look the same?Not enough.
Does one land exactly on the other?Yes means congruent.
Is there still a gap after every slide, turn and flip?Yes means not congruent.

Example: one triangle has sides 5, 6 and 7 cm. Another has sides 5, 6 and 8 cm. The longest sides are 7 cm and 8 cm. They differ by 8 − 7 = 1 cm. So the triangles cannot land.

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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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