AI generatedGeometry and measuresCourse skill

Finding a missing length in overlapping similar triangles

Finding a missing length in overlapping similar triangles.

  • Give a mathematical reason for each step.
  • Use matching angles and corresponding sides, not the appearance of a diagram.
  • State the result you have proved at the end.

Example 1

DE is parallel to . CD = 2 cm, CA = 4 cm and DE = 4 cm. Find .

Overlapping similar trianglesCABDEDE ∥ AB; lengths in cm
CDE and CAB are similar by corresponding angles. Match full CA to CD.Multiply the corresponding smaller length by the scale factor.

Example 2

DE is parallel to . CD = 3 cm, CA = 5 cm and DE = 4 cm. Find .

Overlapping similar trianglesCABDEDE ∥ AB; lengths in cm
CDE and CAB are similar by corresponding angles. Match full CA to CD.Multiply the corresponding smaller length by the scale factor.

Your turn

Question 1

DE is parallel to . CD = 4 cm, CA = 6 cm and DE = 4 cm. Find .

Overlapping similar trianglesCABDEDE ∥ AB; lengths in cm
Check answer
CDE and CAB are similar by corresponding angles. Match full CA to CD.Multiply the corresponding smaller length by the scale factor.
Question 2

DE is parallel to . CD = 5 cm, CA = 7 cm and DE = 4 cm. Find .

Overlapping similar trianglesCABDEDE ∥ AB; lengths in cm
Check answer
CDE and CAB are similar by corresponding angles. Match full CA to CD.Multiply the corresponding smaller length by the scale factor.
Question 3

DE is parallel to . CD = 6 cm, CA = 8 cm and DE = 4 cm. Find .

Overlapping similar trianglesCABDEDE ∥ AB; lengths in cm
Check answer
CDE and CAB are similar by corresponding angles. Match full CA to CD.Multiply the corresponding smaller length by the scale factor.
Question 4

DE is parallel to . CD = 7 cm, CA = 9 cm and DE = 4 cm. Find .

Overlapping similar trianglesCABDEDE ∥ AB; lengths in cm
Check answer
CDE and CAB are similar by corresponding angles. Match full CA to CD.Multiply the corresponding smaller length by the scale factor.
Question 5

DE is parallel to . CD = 2 cm, CA = 4 cm and DE = 5 cm. Find .

Overlapping similar trianglesCABDEDE ∥ AB; lengths in cm
Check answer
CDE and CAB are similar by corresponding angles. Match full CA to CD.Multiply the corresponding smaller length by the scale factor.
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