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 two triangles in the problem. Let's call them Triangle 1 and Triangle 2.
2. Since EA is parallel to CD, use the property of parallel lines to identify corresponding angles. Corresponding angles are equal when a transversal crosses parallel lines.
3. Label the angles in Triangle 1 and Triangle 2. For example, if angle A in Triangle 1 corresponds to angle D in Triangle 2, then angle A = angle D.
4. Identify the corresponding sides of the triangles. Corresponding sides are proportional in similar triangles.
5. List the pairs of corresponding angles and sides. For example, if side AB in Triangle 1 corresponds to side DE in Triangle 2, then AB/DE = BC/EF = CA/FD.

Key Concepts

Similar Triangles

Similar triangles are triangles that have the same shape but may differ in size. This means that their corresponding angles are equal, and their corresponding sides are in proportion. Understanding the properties of similar triangles is essential for identifying corresponding angles and sides, which is crucial in solving problems related to geometry and trigonometry.

Corresponding Angles

Corresponding angles are pairs of angles that are in the same relative position at each intersection where a straight line crosses two others. In the context of parallel lines and transversals, corresponding angles are equal. This concept is vital when analyzing similar triangles, as it helps establish the equality of angles, which is a key characteristic of similarity.

Parallel Lines and Transversals

When a transversal intersects two parallel lines, it creates several pairs of angles, including corresponding angles, alternate interior angles, and consecutive interior angles. The properties of these angles are fundamental in proving that triangles are similar. In the given question, recognizing that EA is parallel to CD allows us to apply these properties to identify corresponding angles and sides in the similar triangles.