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## Similarity Class 10 Maths ICSE Solutions

Download Formulae Handbook For ICSE Class 9 and 10

**Formulae**

**Similarities of triangles:** When two triangles are similar, their corresponding angles are equal and corresponding sides are proportional.

**Axioms of similarity of triangles:** (i.e., three similarity postulates for triangle)

- If two triangles have a pair of corresponding angles equal and the sides including them proportional; then the triangles are similar (SAS postulate).
- If two triangles have two pairs of corresponding angles equal; the triangles are similar (AA or AAA postulate).
- If two triangles have their three pairs of corresponding sides proportional, the triangles are similar (SSS postulate).

**Basic Theorem of Proportionality:**

- A line drawn parallel to any side of a triangle, divides the other two sides proportionally. (Basic proportionality theorem).

**Conversely:**If a line divides two sides of a triangle proportionally, the line is parallel to the third side.

**Relation between the areas of two triangles: Theorem:**The areas of two similar triangles are proportional to the squares on their corresponding sides.

**Determine the Following**

**Question 1.** The model of a building is constructed with scale factor 1:30.

(i) If the height of the model is 80 cm, find the actual height of the building in metres.

(ii) If the actual volume of a tank at the top of the building is 27 m^{3}, find the volume of the tank on the top of the model.

**Question 2.** Triangles ABC and DEF are similar.

**Prove the Following **

**Question 3.** Prove that the area of the triangle BCE described on one side BC of a square ABCD as base is one half of the area of similar triangle ACF described on the diagonal AC as base.

**Question 4.** In figure ABC and DBC are two triangles on the same base BC. Prove that

**Question 5.** In the adjoining figure, the medians BD and CE of a ∆ABC meet at G. Prove that

### Figure Based Questions

**Question 2.** Two isosceles triangle have equal vertical angles and their areas are in the ratio of 36 : 25. Find the ratio between their corresponding heights.

**Question 4.** In the given figure, AB and DE are perpendicular to BC.

**Question 7.** Equilateral triangles are drawn on the sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

**Question 8:** On a map drawn to scale of 1 : 2,50,000 a rectangular plot of land ABCD has the following measurement AB = 12 cm, BC = 16 cm angles A, B, C, and D are 90^{0} each. Calculate:

(i) The diagonal distance of the plot of land in

(ii) Actual length of diagonal.

**Question 10.** In the adjoining figure. BC is parallel to DE, area of ΔABC = 25 sq cm, area of trapezium BCED = 24 sq cm, DE = 14 cm. Calculate the length of BC.

**Question 14.** In the given figure ABC and CEF are two triangles where BA is parallel to CE and AF : AC = 5 : 8.

**Question 16.** Triangles ABC and DEF are similar.

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