# Determine whether the polygons are similar. If so, write a similarity statement and give the scale factor. If not, explain.

Determine whether the polygons are similar. If so, write a similarity statement and give the scale factor. If not, explain.

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Nathanael Webber
In the triangle BCD,
$$\displaystyle\angle{B}={88}^{{\circ}}$$
$$\displaystyle\angle{D}={49}^{{\circ}}$$
$$\displaystyle\angle{C}={180}^{{\circ}}-{\left({88}^{{\circ}}+{49}^{{\circ}}\right)}$$
$$\displaystyle={43}^{{\circ}}$$
In the triangle IJH,
$$\displaystyle\angle{I}={43}^{{\circ}}$$
$$\displaystyle\angle{J}={49}^{{\circ}}$$
$$\displaystyle\angle{H}={180}^{{\circ}}-{\left({43}^{{\circ}}+{49}^{{\circ}}\right)}$$
$$\displaystyle={88}^{{\circ}}$$
Then, $$\displaystyle\angle{B}=\angle{H},\angle{D}=\angle{J},\angle{C}=\angle{I}$$
So, two triangles BCD and IJH will be similar if $$\displaystyle{\frac{{{B}{D}}}{{{H}{J}}}}={\frac{{{B}{C}}}{{{H}{I}}}}={\frac{{{C}{D}}}{{{I}{J}}}}$$
Now,
$$\displaystyle{\frac{{{B}{D}}}{{{H}{J}}}}={\frac{{{6}}}{{{4}}}}$$
$$\displaystyle={\frac{{{3}}}{{{2}}}}$$
$$\displaystyle{\frac{{{B}{C}}}{{{H}{I}}}}={\frac{{{9}}}{{{6}}}}$$
$$\displaystyle={\frac{{{3}}}{{{2}}}}$$
$$\displaystyle{\frac{{{C}{D}}}{{{I}{J}}}}={\frac{{{12}}}{{{8}}}}$$
$$\displaystyle={\frac{{{3}}}{{{2}}}}$$
Since $$\displaystyle{\frac{{{B}{D}}}{{{H}{J}}}}={\frac{{{B}{C}}}{{{H}{I}}}}={\frac{{{C}{D}}}{{{I}{J}}}}$$, triangle BCD and HIJ are similar.