Chapter 06 Triangles Exercise-02
EXERCISE 6.2
1. In Fig. 6.17, (i) and (ii),

Fig. 6.17
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Solution
(i)

Let
It is given that
By using basic proportionality theorem, we obtain
(ii)

Let
It is given that DE || BC.
By using basic proportionality theorem, we obtain
2.
(i)
(ii)
(iii)
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Solution
(i)

Given that,
Hence,
Therefore, EF is not parallel to QR.
(ii)

Hence,
Therefore,
(iii)

Hence,
Therefore, EF is parallel to QR.
3. In Fig. 6.18, if

Fig. 6.18
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Solution

In the given figure,
By using basic proportionality theorem, we obtain
Similarly,
From
4. In Fig. 6.19,

Fig. 6.19
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Solution

In

In
(ii)
From
5. In Fig. 6.20, DE

Fig. 6.20
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Solution

In
(i)

In
From

6. In Fig. 6.21, A, B and

Fig. 6.21
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Solution

In
(i)

In
From

7. Using Theorem 6.1 , prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).
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Solution

Consider the given figure in which
By using basic proportionality theorem, we obtain
Or,
8. Using Theorem 6.2, 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).
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Solution

Consider the given figure in which
i.e.,
It can be observed that
and
Hence, by using basic proportionality theorem, we obtain
9.
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Solution

Draw a line
In
By using basic proportionality theorem, we obtain
In
So, by using basic proportionality theorem, we obtain
From equations (1) and (2), we obtain
10. The diagonals of a quadrilateral
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Solution
Let us consider the following figure for the given question.

Draw a line

In
By using basic proportionality theorem, we obtain
However, it is given that
From equations (1) and (2), we obtain