# NCERT Class 10 Mathematics Similar Triangles Questions CBSE Board Sample Problems

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Question 1.

In , ray AD bisects and intersects BC in D. If and , prove that:

(i)

(ii)

Question 2.

Two poles of heights a and b metres are standing vertically on a level ground r metres a part.

Prove that the height c of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is given by-, i.e.

Question 3.

D and E are points on the sides CA and CB respectively of right — angled at C. Prove that

Question 4.

In a quadrilateral , prove that

Question 5.

ABC is a triangle in which and D is a point on AC such that. Prove that

Question 6.

P and Q are the mid-points on the sides CA and CB respectively of triangle ABC right angled at

C. Prove that

Question 7.

**True and False statement**

a) All quadrilateral triangles are similar.

b) All circles are similar.

c) All isosceles triangles are similar.

d) All triangles are similar.

Question 8.

In the below figure PA, QB and RC are each perpendicular to AC.

Prove that

Question 9.

ABC is a right triangle right angled at C. Let and let p be the length of perpendicular from C on AB, prove that

(i)

(ii)

Question 10.

Diagonals of a trapezium ABCD with ABIIDC intersect each other at the point O. If , find ratio of the areas of AOB and COD