Triangles

In $\triangle ABC$, $DE \parallel BC$ where $D$ and $E$ are points on $AB$ and $AC$ respectively. If $AD = 2\text{ cm}$, $DB = 3\text{ cm}$, and $AE = 1.6\text{ cm}$, find the length of $EC$.

Which of the following is NOT a valid criterion for the similarity of two triangles as per the Grade 10 curriculum?

If $\triangle ABC \sim \triangle PQR$ such that the ratio of their corresponding sides $\frac{AB}{PQ} = \frac{1}{3}$, what is the ratio of their perimeters?

For any two similar triangles, the ratio of any two corresponding sides is called the:

If $\Delta ABC \sim \Delta DEF$, $AB = 4$, $BC = 3.5$, $CA = 2.5$, and $DF = 7.5$, find $DE$.

Two triangles are similar if their corresponding ______ are proportional.

In $\triangle DEF$, $GH \parallel EF$. If $DG = 2$ cm, $GE = 3$ cm, and $DH = 4$ cm, find the length of $DF$.

In $\triangle ABC$, $PQ \parallel BC$. If $AP = x$, $PB = x + 2$, $AQ = x + 1$, and $QC = x + 4$, find $x$.

In $\triangle LMN$, $XY \parallel MN$. If $LX = 2.5$ cm, $XM = 5$ cm, and $LN = 9$ cm, find $LY$.