Question

In the given figure, line a || line b || line c. Line d and line e are their transversals and intersect them at points P, Q, R and L, M, N, respectively. Point Q is the midpoint of seg PR. If l(QR) = 7.2 and l(LM) = 6.2, find l(PQ) and l(MN).

Answer 1

Given: line a || line b || line c
Transversals line d and line e cut the lines at points P, Q, R and L, M, N, respectively.
Point Q is the mid-point of segment seg PR; QR = 7.2 cm
l(LM) = 6.2
To find: l(PQ) and l(MN)
Since point Q is the mid-point of segment seg PR, PQ = QR.
QR = 7.2 cm; so, PQ = QR = 7.2 cm
According to the property of three parallel lines and their transversals,
$$\begin{gathered} \frac{l\left(\mathrm{PQ}\right)}{l\left(\mathrm{QR}\right)}=\frac{l\left(\mathrm{LM}\right)}{l\left(\mathrm{MN}\right)} \\ \therefore \frac{7.2}{7.2}=\frac{6.2}{l\left(\mathrm{MN}\right)} \\ \therefore 1=\frac{6.2}{l\left(\mathrm{MN}\right)} \\ \therefore l\left(\mathrm{MN}\right)=6.2 \end{gathered}$$
∴ l(PQ) = 7.2 and l(MN) = 6.2