EXERCISE 6.2
Q-1(i), Ex 6.2 - Triangles - Chapter 6 - Maths Class 10th - NCERT
Q-1(ii), Ex 6.2 - Triangles - Chapter 6 - Maths Class 10th - NCERT
Page No 128:
Question 1:
In figure.6.17. (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).(i)
(ii)
Answer:
(i)
Let EC = x cm
It is given that DE || BC.
By using basic proportionality theorem, we obtain
(ii)
Let AD = x cm
It is given that DE || BC.
By using basic proportionality theorem, we obtain
Q 2, Ex 6.2 - Triangles - Chapter 6 - Maths Class 10th - NCERT
Question 2:
E and F are points on the sides PQ and PR respectively of a ΔPQR. 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 = 0.63 cm
Answer:
(i)
Given that, PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm, FR = 2.4 cm
(ii)
PE = 4 cm, QE = 4.5 cm, PF = 8 cm, RF = 9 cm
(iii)
PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm, PF = 0.36 cm
Q 3, Ex 6.2 - Triangles - Chapter 6 - Maths Class 10th - NCERT
Question 3:
In the following figure, if LM || CB and LN || CD, prove that
Answer:
In the given figure, LM || CB
By using basic proportionality theorem, we obtain
Q 4, Ex 6.2 - Triangles - Chapter 6 - Maths Class 10th - NCERT
Question 4:
In the following figure, DE || AC and DF || AE. Prove that
Answer:
In ΔABC, DE || AC
Q 5, Ex 6.2 - Triangles - Chapter 6 - Maths Class 10th - NCERT
Page No 129:
Question 5:
In the following figure, DE || OQ and DF || OR, show that EF || QR.
Answer:
In Δ POQ, DE || OQ
Q 6, Ex 6.2 - Triangles - Chapter 6 - Maths Class 10th - NCERT
Question 6:
In the following figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.
Answer:
In Δ POQ, AB || PQ
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. (Recall that you have proved it in Class IX).Answer:
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Consider the given figure in which l is a line drawn through the mid-point P of line segment AB meeting AC at Q, such that
.
Or, Q is the mid-point of AC.
Q 8, Ex 6.2 - Triangles - Chapter 6 - Maths Class 10th - NCERT
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).Answer:
Consider the given figure in which PQ is a line segment joining the mid-points P and Q of line AB and AC respectively.
i.e., AP = PB and AQ = QC
It can be observed that
Hence, by using basic proportionality theorem, we obtain
Q 9, Ex 6.2 - Triangles - Chapter 6 - Maths Class 10th - NCERT
Question 9:
ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that
Answer:
Draw a line EF through point O, such that
In ΔADC,
By using basic proportionality theorem, we obtain
In ΔABD,
So, by using basic proportionality theorem, we obtain
From equations (1) and (2), we obtain
Q 10, Ex 6.2 - Triangles - Chapter 6 - Maths Class 10th - NCERT
Question 10:
The diagonals of a quadrilateral ABCD intersect each other at the point O such that
Show that ABCD is a trapezium.Answer:
Let us consider the following figure for the given question.
Draw a line OE || AB
In ΔABD, OE || AB
By using basic proportionality theorem, we obtain
However, it is given that
⇒ EO || DC [By the converse of basic proportionality theorem]
⇒ AB || OE || DC
⇒ AB || CD
∴ ABCD is a trapezium.
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