**Selina Concise Mathematics Class 10 ICSE Solutions Similarity (With Applications to Maps and Models)**

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**Selina ICSE Solutions for Class 10 Maths Chapter 15 Similarity (With Applications to Maps and Models)**

**Exercise 15(A)**

**Question 1.
**(i)

(ii)

**Question 2.
**(i)

(ii)

**Question 3.
**(i)

(ii)

**Question 4.
**(i)

(ii)

**Question 5.
**(i)

(ii)

**Question 6.**

**Question 7.
**(i)

(ii)

**Question 8.**

**Question 9.**

**Question 10.**

**Question 11.**

State, true or false:

(i) Two similar polygons are necessarily congruent.

(ii) Two congruent polygons are necessarily similar.

(iii) All equiangular triangles are similar.

(iv) All isosceles triangles are similar.

(v) Two isosceles-right triangles are similar.

(vi) Two isosceles triangles are similar, if an angle of one is congruent to the corresponding angle of the other.

(vii) The diagonals of a trapezium, divide each other into proportional segments.

**Solution:**

(i) False

(ii) True

(iii) True

(iv) False

(v) True

(vi) True

(vii) True

**Question 12.**

**Solution:**

**Question 13.**

**Solution:**

**Question 14.**

**Solution:**

**Question 15.**

**Solution:**

**Question 16.**

**Solution:**

**Question 17.**

**Solution:**

**Question 18.**

**Solution:**

**Question 19.**

**Solution:**

**Question 20.**

**Solution:**

**Question 21.**

In quadrilateral ABCD, diagonals AC and BD intersect at point E such that AE: EC = BE: ED. Show that ABCD is a trapezium.

**Solution:**

**Question 22.**

**Solution:**

**Question 23.**

**Solution:**

**Question 24.**

**Solution:**

**Question 25.**

Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting diagonal AC in L and AD produced in E. Prove that: EL = 2BL.

**Solution:**

**Question 26.**

**Solution:**

**Question 27.**

**Solution:**

**Question 28.**

**Solution:**

**Exercise 15(B)**

**Solution 1(i).**

**Solution 1(ii).**

**Solution 1(iii).**

**Solution 1(iv).**

**Solution 1(v).**

**Solution 2(i).**

**Solution 2(ii).**

**Solution 2(iii).**

**Solution 3.**

**Solution 4(i).**

**Solution 4(ii).**

**Solution 5.**

**Solution 6.**

**Solution 7.**

**Solution 8.**

**Solution 9.**

**Solution 10.**

**Exercise 15(C)**

**Question 1.**

(i) The ratio between the corresponding sides of two similar triangles is 2 is to 5. Find the ratio between the areas of these triangles.

(ii) Areas of two similar triangles are 98 sq. cm and 128 sq. cm. Find the ratio between the lengths of their corresponding sides.

**Solution:**

**Question 2.**

**Solution:**

**Question 3.**

The perimeters of two similar triangles are 30 cm and 24 cm. If one side of the first triangle is 12 cm, determine the corresponding side of the second triangle.

**Solution:**

**Question 4.**

**Solution:**

**Question 5.**

ABC is a triangle. PQ is a line segment intersecting AB in P and AC in Q such that PQ || BC and divides triangle ABC into two parts equal in area. Find the value of ratio BP: AB.

**Solution:**

**Question 6.**

**Solution:**

**Question 7.**

**Solution:**

**Question 8.**

**Solution:**

**Question 9.**

**Solution:**

**Question 10.**

**Solution:**

**Question 11.**

**Solution:**

**Question 12.**

**Solution:**

**Question 13.**

**Solution:**

**Exercise 15(D)**

**Question 7.**

**Solution:**

**Question 8.**

**Solution:**

**Exercise 15(E)**

**Question 8.**

**Solution:**

**Question 15.**

**Solution:**

**Question 16.**

**Solution:**

**Question 17.**

**Solution:**

**Question 18.**

Two similar triangles are equal in area. Prove that the triangles are congruent.

**Solution:**

**Question 19.**

The ratio between the altitudes of two similar triangles is 3: 5; write the ratio between their:

(i) medians. (ii) perimeters. (iii) areas.

**Solution:**

**Question 20.**

The ratio between the areas of two similar triangles is 16: 25. Find the ratio between their:

(i) perimeters. (ii) altitudes. (iii) medians.

**Solution:**

**Question 21.**

**Solution:**

**Question 22.**

On a map drawn to a scale of 1: 20000, a rectangular plot of land ABCD is measured as AB = 24 cm and BC = 32 cm. Calculate:

(i) the diagonal distance of the plot in kilometre.

(ii) the area of the plot in sq. km.

**Solution:**

**Question 23.**

**Solution:**

**Question 24.**

**Solution:**

**Question 25.**

**Solution:**

**Question 26.**

**Solution:**

**Question 27.**

Two isosceles triangles have equal vertical angles. Show that the triangles are similar.

If the ratio between the areas of these two triangles is 16: 25, find the ratio between their corresponding altitudes.

**Solution:**

**Question 28.**

**Solution:**

**Question 29.**

**Solution:**

**Question 30.**

**Solution:**

**Question 31.**

**Solution:**

**Question 34.**

**Solution:**

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