Question

The map given below shows five different villages. Village M lies exactly halfway between the two pairs of villages A and B as well as and P and Q. What is the distance between village A and village P. (Hint: check if $\Delta PAM\cong \Delta QBM$)

Answer 1

Village M lies in between A and B

$\therefore AM=BM$ __(1)

Also, village M lies in between P and Q.

$\therefore PM=QM$ __(2)

In $\Delta PAM$ and $\Delta QBM$,

$AM=BM$ (from (1))

$PM=QM$ (From (2))

$\angle AMP=\angle BMQ$ (vertically opposite angles)

$\therefore$ By SAS congruency,

$\Delta PAM\cong \Delta QBM$

$\because AP=BQ=4km$