Question

PQ is perpendicular bisector if ST. Find the values of m and n.

Answer 1

The given parallelogram is a Rhombus, with characteristics

1- The diagonals bisect each other at the midpoint.

2- Each diagonal divides it into two congruent triangles

3- All the sides of the Rhombus are of equal lenght.

PQ divides the figure into two congruent triangles, then the corresponding sides are equal.

If PS=TP, then

`\begin{gathered} 3m+9=5m-13 \\ 3m-5m=-13-9 \\ -2m=-22 \\ -(2m)/(-2)=-(22)/(-2) \\ m=11 \end{gathered}`

If SQ=QT, then

`\begin{gathered} 6n-3=4n+14 \\ 6n-4n=14+3 \\ 2n=17 \\ (2n)/(2)=(17)/(2) \\ n=8.5 \end{gathered}`