In trapezium ABCD, BC ∥ AD and AD = 4 cm. Diagonals AC and BD meet at O such that AO/OC = DO/OB = 1/2. Find the length of BC.

In ΔABC, L and M are two points on the sides AC and BC respectively such that LM || AB and AL are (x - 2) units, AC = 2x + 3 units, BM = (x – 3) units and BC = 2x units. Determine the value of x.

DE ∥ BC of ΔABC where D and E are two points on AB and AC, respectively. If AD = 5 cm, DB = 6 cm, and AE = 7.5 cm, calculate the length of AC.

If the lengths of three sides of two triangles are in proportion, then which type of triangle is this?

Two triangles are similar if their corresponding sides are ___.

In the given figure, AC ∥ DE ∥ BF. If AC = 24 cm, EG = 8 cm, GB = 16 cm and BF = 30 cm: (a) Prove △GED ∼ △GBF (b) Find DE (c) Find DB : AB.

In the given diagram, DE ∥ BC and AD : DB = 2 : 3. (a) Prove that: ΔADE ~ ΔABC and hence find DE : BC. (b) Prove: ΔDFE ~ ΔCFB. (c) Given, area of ΔDFE = 16 square units, find the area of ΔCFB.

The areas of two similar triangles are in the ratio 9 : 64. The ratio of their corresponding altitudes is: (a) 3 : 8 (b) 2 : 1 (c) 9 : 64 (d) 8 : 3

In △ABC, ∠ABC = 90°, AB = 20 cm and AC = 25 cm. DE is perpendicular to AC such that ∠DEA = 90° and DE = 3 cm, as shown. (a) Prove that △ABC ∼ △AED. (b) Find BC, AD and AE. (c) If BCED represents land on a map whose actual area is 576 m², find the scale factor of the map.

In the given diagram, △ABC ∼ △EFG. If ∠ABC = ∠EFG = 60°, then the length of side FG is: (a) 15 cm (b) 20 cm (c) 25 cm (d) 30 cm

In the given diagram, △ABC ∼ △PQR. If AD and PS are bisectors of ∠BAC and ∠QPR respectively, then: (a) △ABC ∼ △PQS (b) △ABD ∼ △PQS (c) △ABD ∼ △PSR (d) △ABC ∼ △PSR

In the given diagram, △ADB and △ACB are two right-angled triangles with ∠ADB = ∠BCA = 90°. If AB = 10 cm, AD = 6 cm, BC = 2.4 cm and DP = 4.5 cm: (a) Prove that △APD ∼ △BPC. (b) Find the lengths of BD and PB. (c) Hence, find the length of PA. (d) Find area of △APD : area of △BPC.