01 · CBSE BOARD EXAM 2024
CBSE 2024 Board Practice Questions
CBSE 2024 · 1 MARK
Q1. In △ABC, DE ∥ BC such that AD = 3 cm, DB = 5 cm and AE = 4.5 cm. Find EC.
CBSE 2024 · 1 MARK
Q2. If △ABC ~ △PQR with AB / PQ = 1 / 3, then find ar(△ABC) / ar(△PQR).
CBSE 2024 · 2 MARKS
Q3. In a trapezium ABCD, AB ∥ DC and its diagonals intersect each other at point O. Show that AO / BO = CO / DO.
CBSE 2024 · 3 MARKS
Q4. State and prove Basic Proportionality Theorem (Thales Theorem).
CBSE 2024 · 5 MARKS
Q5. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio. Using this theorem, in △ABC with DE ∥ BC, if AD/DB = 3/5 and AC = 5.6 cm, find AE.
02 · CBSE BOARD EXAM 2023
CBSE 2023 Board Practice Questions
CBSE 2023 · 1 MARK
Q6. Sides of two similar triangles are in the ratio 4 : 9. Ratio of their areas is:
(A) 2 : 3 (B) 4 : 9 (C) 81 : 16 (D) 16 : 81
CBSE 2023 · 2 MARKS
Q7. E and F are points on the sides PQ and PR respectively of a △PQR. For PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm, check if EF ∥ QR.
CBSE 2023 · 3 MARKS
Q8. In △ABC, D and E are points on sides AB and AC respectively such that DE ∥ BC. If AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, find the value of x.
CBSE 2023 · 5 MARKS
Q9. Diagonals of a quadrilateral ABCD intersect each other at point O such that AO / BO = CO / DO. Prove that ABCD is a trapezium.
03 · CBSE BOARD EXAM 2022
CBSE 2022 Board Practice Questions
CBSE 2022 · 1 MARK
Q10. Two triangles △ABC and △DEF are similar such that ∠A = 47° and ∠E = 83°. Find ∠C.
CBSE 2022 · 2 MARKS
Q11. In given △ABC, DE ∥ BC. If AD = 2.4 cm, AE = 3.2 cm, EC = 4.8 cm, find BD.
CBSE 2022 · 3 MARKS
Q12. In △ABC, ∠A = 90° and AD ⊥ BC. Prove that AD² = BD · CD.
04 · CBSE BOARD EXAM 2021
CBSE 2021 Board Practice Questions
CBSE 2021 · 1 MARK
Q13. Are two isosceles triangles always similar? State true or false with reason.
CBSE 2021 · 2 MARKS
Q14. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.
CBSE 2021 · 3 MARKS
Q15. Through the vertex D of a parallelogram ABCD, a line is drawn to intersect the side BC at P and AB produced at Q. Prove that DA · PQ = FB · DP.
05 · CBSE BOARD EXAM 2020
CBSE 2020 Board Practice Questions
CBSE 2020 · 1 MARK
Q16. In △ABC, D and E are points on AB and AC such that DE ∥ BC. If AD/DB = 2/3 and AC = 18 cm, find AE.
CBSE 2020 · 3 MARKS
Q17. In △ABC, if AD ⊥ BC, prove that AB² + CD² = AC² + BD².
CBSE 2020 · 5 MARKS
Q18. State and prove the Converse of Basic Proportionality Theorem.
06 · SELF-PRACTICE TIPS
Tips for Solving Board PYQs
01
Always draw a clear, labeled triangle diagram before starting any geometry proof.
02
For BPT problems, write AD/DB = AE/EC and substitute given values accurately.
03
When proving similarity, state the criterion used (AA, SSS, or SAS) explicitly.