Problems on similar triangles for class 10

Given below are the Similar Triangles Class 10 Problems and questions with Answer
a. Proof Questions
b. Calculation problems
c. True & False Questions
d. Fill in the blanks

Proof Problems/word Problems

Question 1.
In $\Delta ABC$ , ray AD bisects $ \angle A$ and intersects BC in D. If BC = a, AC = b and AB = c, prove that:
i. $BD = \frac {ac}{b+c}$
ii.$DC = \frac {ab}{c+b}$

Question 2.
Two poles of heights a and b metres are standing vertically on a level ground r metres apart. 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 $\frac {ab}{a+b}$ i.e $c = \frac {ab}{a+b}$

Question 3.
D and E are points on the sides CA and CB respectively of $\Delta ABC$ right-angled at C. Prove that $AE^2 + BD^2 = AB^2 + DE^2$

Question 4.
In a quadrilateral ABCD, $\angle B = 90$ , $AD^2= AB^2 + BC^2 + CD^2$, prove that $\angle ACD = 90$

Question 5.
ABC is a triangle in which AB = AC and D is a point on AC such that
$BC^2 =AC \times CD$ . Prove that BD=BC

Question 6.
ABC is a right triangle right angled at C. Let BC = a, CA = b AB = c and let p be the length of perpendicular from C on AB, prove that
(i) $cp = ab$
(ii) $ \frac {1}{p^2}= \frac {1}{a^2}+ \frac {1}{b^2}$

Question 7.
In the below figure PA, QB and RC are each perpendicular to AC.
Prove that
$ \frac {1}{x} + \frac {1}{y} = \frac {1}{z}$

Calculation Problems

Question 8.
if $ \Delta ABC \sim \Delta DEF$ and their sides are of lengths (in cm) as marked along them, then find the lengths of the sides of each triangle.

Question 9.
Diagonals of a trapezium ABCD with AB||DC intersect each other at the point O. If AB = 2DC, find ratio of the areas of AOB and COD

True and False

Question 10.
True and False statement
(a) All quadrilateral are similar.
(b) All circles are similar.
(c ) All isosceles triangles are similar.
(d) All 30°, 60°, 90° triangles are similar.

Fill in the blanks

Question 11.
(a) when two triangles are similar, then their corresponding altitudes are in the same _________.
(b) The ratio of the perimeters of two similar triangles is equal to the ratio of their corresponding _________.
(c) If in two triangles ABC and PQR,$\frac {AB}{QR}=\frac {BC}{PR}=\frac {CA}{PQ}$, then $\Delta PQR \sim $ _____.
(d) In two similar triangles, the corresponding angles are _________.


This Class 10 Maths Problems for Similar triangles with answers is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail.You can download in PDF form also using the below links

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Also Read

Go back to Class 10 Main Page using below links
Class 10 Maths Class 10 Science

Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20

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