CONCEPT PREVIEW Name the corresponding angles and the corresponding sides of each pair of similar triangles.

검증된 단계별 안내

Recall that similar triangles have the same shape but not necessarily the same size. This means their corresponding angles are equal, and their corresponding sides are proportional.

Identify the pairs of triangles given in the problem and label their vertices clearly, for example, triangle ABC and triangle DEF.

Match the corresponding angles by comparing the order of vertices in the triangles. For instance, angle A corresponds to angle D, angle B corresponds to angle E, and angle C corresponds to angle F.

Once the corresponding angles are identified, determine the corresponding sides by looking at the sides opposite those angles. For example, side AB corresponds to side DE, side BC corresponds to side EF, and side AC corresponds to side DF.

Write down the pairs of corresponding angles and sides explicitly, such as: angles \(\angle A \leftrightarrow \angle D\), \(\angle B \leftrightarrow \angle E\), \(\angle C \leftrightarrow \angle F\) and sides \(AB \leftrightarrow DE\), \(BC \leftrightarrow EF\), \(AC \leftrightarrow DF\).

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주요 개념

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Similar Triangles

Similar triangles have the same shape but not necessarily the same size. Their corresponding angles are equal, and their corresponding sides are proportional. Recognizing similarity helps in identifying angle and side correspondences.

Corresponding Angles

Corresponding angles in similar triangles are pairs of angles that occupy the same relative position in each triangle. These angles are congruent, meaning they have equal measures, which is key to establishing similarity.

Corresponding Sides

Corresponding sides in similar triangles are the sides opposite the corresponding angles. These sides are proportional, meaning the ratios of their lengths are equal. Understanding this helps in solving for unknown side lengths.