9-1 Lesson Check: Similar Polygons (LMS graded) \[ \begin{array}{l}\text { Part } 1 \text { of } 2 \\ \begin{array}{l}\text { List the pairs of congruent angles and the extended } \\ \text { proportion that relates the corresponding sides for the } \\ \text { similar triangles. }\end{array} \\ \Delta A B C \sim \Delta H I J\end{array} \]

In triangles \( \Delta ABC \) and \( \Delta HIJ \), the pairs of congruent angles are \( \angle A \cong \angle H \), \( \angle B \cong \angle I \), and \( \angle C \cong \angle J \). This means that each angle in triangle ABC has a corresponding equal angle in triangle HIJ, showing their similarity. For the extended proportion relating the corresponding sides, you can express it as follows: \( \frac{AB}{HI} = \frac{BC}{IJ} = \frac{AC}{HJ} \). This proportion tells us that the ratios of the lengths of the sides of triangle ABC to the corresponding sides of triangle HIJ are equal, adhering to the properties of similar polygons!