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

Verified step by step guidance

1. Identify the pairs of similar triangles in the figure, noting that since EA is parallel to CD, corresponding angles formed by a transversal are congruent.
2. Name the corresponding angles by matching angles that are equal due to parallel lines and similarity. For example, if angle E corresponds to angle C, and angle A corresponds to angle D, list these pairs explicitly.
3. Identify the corresponding sides by looking at the sides opposite the corresponding angles. For instance, the side opposite angle E in one triangle corresponds to the side opposite angle C in the other triangle.
4. Write down the pairs of corresponding sides, such as EA corresponding to CD, and any other sides that match based on the angle correspondences.
5. Summarize the pairs of corresponding angles and sides clearly, emphasizing the relationship established by the parallel lines and the similarity of the triangles.

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 identify matching angles and sides between two triangles.

Corresponding Angles

Corresponding angles are pairs of angles that occupy the same relative position in two similar or congruent figures. In the context of parallel lines and transversals, corresponding angles are equal, which helps in identifying angle pairs in similar triangles.

Parallel Lines and Transversals

When a transversal crosses parallel lines, it creates pairs of equal corresponding angles. This property is essential for proving triangle similarity and determining which angles and sides correspond between triangles.