Enter the proportional segment lengths into the boxes to verify that ¯¯¯QS¯∥MN¯ . ___ /1.5= ___ / ___?
Two triangles RMN & RQS are similar.
Therefore, QS // MN.
To prove QS is parallel to MN.
Add 1 to both sides,
Dividing Eqn (1) by (2),
Two sides of triangles RMN & RQS are in the same proportion.
Therefore third sides are also in the same proportion.
That means both the triangles RMN & RQS are similar and hence
MN // QS.