Class 10 / Maths

Class 10 Maths Triangles Worksheet

Practice triangle similarity, proportional sides, BPT, Pythagoras theorem, and area ratios.

advanced50 minutesAnswer key included

Learning objective

Practise similarity criteria, proportional sides, BPT, Pythagoras theorem, area ratios, and theorem-based reasoning.

Questions

  1. State the AA, SSS, and SAS similarity criteria.
  2. If triangle ABC is similar to triangle PQR and AB/PQ = 2/3, find BC/QR.
  3. Two similar triangles have corresponding sides in the ratio 4:5. Find the ratio of their areas.
  4. Check whether triangles with sides 3, 4, 5 and 6, 8, 10 are similar.
  5. In triangle ABC, DE is parallel to BC. If AD = 3 cm, DB = 6 cm, and AE = 4 cm, find EC.
  6. Use Pythagoras theorem to find the hypotenuse of a right triangle with legs 8 cm and 15 cm.
  7. Check whether 7 cm, 24 cm, and 25 cm can be sides of a right triangle.
  8. If the hypotenuse is 13 cm and one side is 5 cm, find the other side.
  9. If areas of two similar triangles are 25 sq cm and 64 sq cm, find the ratio of corresponding sides.
  10. Write one real-life situation where similar triangles can be used.

Answer key

Show suggested answers
  1. AA: two corresponding angles equal. SSS: three pairs of corresponding sides proportional. SAS: one included angle equal and surrounding side pairs proportional.
  2. Since the triangles are similar, BC/QR = AB/PQ = 2/3.
  3. Area ratio = square of side ratio = 16:25.
  4. Yes, they are similar because 3/6 = 4/8 = 5/10 = 1/2.
  5. By BPT, AD/DB = AE/EC. So 3/6 = 4/EC, giving EC = 8 cm.
  6. Hypotenuse = sqrt(8^2 + 15^2) = sqrt(289) = 17 cm.
  7. Yes. 7^2 + 24^2 = 49 + 576 = 625 = 25^2.
  8. Other side = sqrt(13^2 - 5^2) = sqrt(144) = 12 cm.
  9. Side ratio = sqrt(25/64) = 5:8.
  10. Similar triangles can be used to estimate the height of a building or tree using shadows.

How to use this worksheet

Students can solve the questions independently first, then review errors with a parent or teacher. Teachers can use it as a short class activity, homework sheet, or revision check.

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