Question

In $∆$ABC, (see fig. 5.13) X, Y and Z are the mid-points of side AB, side BC and side AC respectively.
AB = 5cm, AC = 9cm and BC = 11cm.
Find (i) XY (ii) YZ (iii) XZ.

Answer 1

Since, X , Y and Z are mid points of side AB, side BC and side AC respectively .

By the mid point theorem, we have:

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{XY}=\frac{1}{2}\mathrm{AC} \\ =\frac{1}{2}\left(9\right) \\ =4.5\mathrm{cm} \\ \left(\mathrm{ii}\right)\mathrm{YZ}=\frac{1}{2}\mathrm{AB} \\ =\frac{1}{2}\left(5\right) \\ =2.5\mathrm{cm} \\ \left(\mathrm{iii}\right)\mathrm{XZ}=\frac{1}{2}\mathrm{BC} \\ =\frac{1}{2}\left(11\right) \\ =5.5\mathrm{cm} \end{gathered}$$