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Triangles

Which test decides it

A card lists measurements for two triangles. Are they similar? Match the corners first.

P pairs with Z, R with Y, and Q with X.

Three tests

Use AA, SSS or SAS to decide if two triangles are similar.

Match the corners first. Two matching angles give AA. Three side ratios give SSS. Two side ratios with the angle between them give SAS.

Three tests and what each needs
TestNeeds
AATwo matching angles
SSSAll three side ratios equal
SASTwo side ratios and the angle between them

Read the figure

The 50° corners are P and Z. The 60° corners are R and Y. So P pairs with Z, and R pairs with Y. That leaves Q paired with X. Both third angles are 70°. AA decides it. Triangle PQR is similar to triangle ZXY.

Sometimes no test applies. One angle pair alone is not a test. Two side ratios without the angle between them are not a test.

Pick the test for seven cards.

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This track

  1. 0 Start here
  2. 1 Similar, said precisely
  3. 2 Two angles are enough
  4. 3 Sides in the same ratio
  5. 4 Two sides and the angle between
  6. 5 Heights without ladders
  7. 6 Checkpoint: shapes, factors and shadows
  8. 7 A line parallel to one side
  9. 8 Reading the split backwards
  10. 9 Checkpoint: the parallel-line pair
  11. 10 From a parallel to a similarity
  12. 11 Which test decides it
  13. 12 The big picture
  14. 13 Track quiz

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