CONCEPT PREVIEW Name the corresponding angles and the corresponding sides of each pair of similar triangles. (HK is parallel to EF.)

Verified step by step guidance

1. Identify the pairs of similar triangles in the figure. Since HK is parallel to EF, triangles formed by these lines and the transversal lines are similar by the AA (Angle-Angle) similarity criterion.
2. Name the corresponding angles of the similar triangles. Corresponding angles are those that occupy the same relative position in each triangle. For example, if angle H corresponds to angle E, then angle K corresponds to angle F, and the third angles correspond as well.
3. Name the corresponding sides of the similar triangles. Corresponding sides are opposite the corresponding angles. For instance, if side HK corresponds to side EF, then side adjacent to angle H corresponds to the side adjacent to angle E, and so on.
4. Use the parallel lines property to justify the angle correspondences. Since HK is parallel to EF, alternate interior angles and corresponding angles formed by the transversal lines are congruent, confirming the similarity.
5. Write down the pairs of corresponding angles and sides explicitly, such as: angle H corresponds to angle E, side HK corresponds to side EF, and so forth, to clearly establish the similarity mapping.

Key Concepts

Similar Triangles

Similar triangles have the same shape but not necessarily the same size, meaning their corresponding angles are equal and their corresponding sides are proportional. Recognizing similarity allows us to match angles and sides between triangles.

Corresponding Angles

Corresponding angles are pairs of angles in two triangles that occupy the same relative position. In similar triangles, these angles are congruent, which helps identify which angles correspond between the two figures.

Parallel Lines and Transversals

When a line is parallel to another (e.g., HK parallel to EF), it creates equal corresponding angles with transversals intersecting them. This property helps establish angle congruence and thus similarity between triangles.