Exercise 6.2 Class 10 Maths Chapter 6 Triangles Solution

6. In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

Answer:

To prove BC || QR, we need to show corresponding angles ∠BOC & ∠OQR are equal. This is possible only when ∆OBC ~ ∆OQR. So, we need to prove that ∆OBC ~ ∆OQR.

Now as given,

∆OAB ~ ∆OPQ; So, OB/OQ = OA/OP = AB/PQ (i)

∆OAC ~ ∆OPR; So, OC/OR = OA/OP = AC/PR (ii)

In finding i and ii OA/OP is common, So:

OB/OQ = OC/OR

∠BOC = ∠OQR

Two sides in equal ratio and one same angle make two triangles similar. So,∆OBC ~ ∆OQR.
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).

Next: Exercise 6.3, Class 10 Maths Chapter 6, Triangles Solution.

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6. In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

Two sides in equal ratio and one same angle make two triangles similar. So,∆OBC ~ ∆OQR. 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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Two sides in equal ratio and one same angle make two triangles similar. So,∆OBC ~ ∆OQR.
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).