Question

The two triangles shown are similar. Write all the proportions that are true about these two triangles.

Answer 1

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion, therefore:

$\begin{gathered} k\cdot AB=A^{\prime}B^{\prime} \\ k\cdot AC=A^{\prime}C^{\prime} \\ k\cdot BC=B^{\prime}C^{\prime} \end{gathered}$

Where:

k = Constant of proportionality

Example:

Let's assume those triangles are similar, then the proportions are given by:

$\begin{gathered} k\cdot AB=XY \\ k\cdot AC=XZ \\ k\cdot BC=YZ \end{gathered}$