In Fig. 6.17, (i) and (ii), DE \(\parallel\) BC. Find EC in (i) and AD in (ii).
(i) \(2\ \text{cm}\)
(ii) \(2.4\ \text{cm}\)
E and F are points on the sides PQ and PR respectively of a \(\triangle PQR\). For each of the following cases, state whether \(EF \parallel QR\):
(i) No
(ii) Yes
(iii) Yes
In Fig. 6.18, if LM \(\parallel\) CB and LN \(\parallel\) CD, prove that
\[\frac{AM}{AB} = \frac{AN}{AD}.\]
\(\dfrac{AM}{AB} = \dfrac{AN}{AD}\)
In Fig. 6.19, DE \(\parallel\) AC and DF \(\parallel\) AE. Prove that
\[\frac{BF}{FE} = \frac{BE}{EC}.\]
\(\dfrac{BF}{FE} = \dfrac{BE}{EC}\)
In Fig. 6.20, DE \(\parallel\) OQ and DF \(\parallel\) OR. Show that \(EF \parallel QR\).
\(EF \parallel QR\)
In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively such that AB \(\parallel\) PQ and AC \(\parallel\) PR. Show that BC \(\parallel\) QR.
\(BC \parallel QR\)
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).
A line drawn through the mid-point of one side of a triangle and parallel to another side bisects the third side.
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).
The line joining the mid-points of any two sides of a triangle is parallel to the third side.
ABCD is a trapezium in which AB \(\parallel\) DC and its diagonals intersect each other at the point O. Show that
\[\frac{AO}{BO} = \frac{CO}{DO}.\]
Through O, draw a line parallel to DC, intersecting AD and BC at E and F respectively.
The diagonals of a quadrilateral ABCD intersect each other at the point O such that
\[\frac{AO}{BO} = \frac{CO}{DO}.\]
Show that ABCD is a trapezium.
ABCD is a trapezium with \(AB \parallel CD\).