NCERT Class 10 Maths Solutions Chapter - 6 Triangles, Ex - 6.2

Ex - 6.2

Question 1.  In figure. (i) and (ii) below, DE || BC. Find EC in (i) and AD in (ii).


Solution

(i) 
 
Let EC = x
Since DE || BC.
Therefore, by basic proportionality theorem,


(ii)

Let AD = x 
Since DE || BC,
Therefore by basic proportionality theorem,


Question 2.  E and F are points on the sides PQ and PR respectively of a PQR. For each of the following cases, state whether EF || QR.
 (i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm
 (ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm
 (iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm

Solution

(i) 

Given that PE = 3.9, EQ = 3, PF = 3.6, FR = 2.4
Now, 

(ii)

PE = 4, QE = 4.5, PF = 8, RF = 9


(iii) 

PQ = 1.28, PR = 2.56, PE = 0.18, PF = 0.36


Question 3.  In figure, if LM || CB and LN || CD, prove that


Solution


In the given figure
Since LM || CB,
Therefore by basic proportionality theorem,


Question 4.  In figure , DE || AC and DF || AE. Prove that


Solution


In ABC,
Since DE || AC 



Question 5.  In figure , DE || OQ and DF || OR, show that EF || QR.



Solution


In POQ
Since DE || OQ





Question 6.



Solution


Question 7.  Using Basic proportionality Theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side.

Solution


Consider the given figure 
PQ is a line segment drawn through midpoint P of line AB such that PQ||BC
i.e. AP = PB
Now, by basic proportionality theorem 
 
i.e. AQ = QC
Or, Q is midpoint of AC.

Question 8.  Using converse of Basic Proportionality Theorem, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX).

Solution



Consider the given figure 
PQ is a line segment joining midpoints P and Q of line AB and AC respectively.
i.e. AP = PB and AQ = QC
Now, we may observe that 
 
And hence basic proportionality theorem is verified
So, PQ||BC

Question 9.  ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that


Solution



Question 10.  The diagonals of a quadrilateral ABCD intersect each other at the point O such thatShow that ABCD is a trapezium.

Solution

Ex-6.3