What is true about corresponding angles and corresponding angles and corresponding sides of similar figures?
In similar figures, corresponding angles are congruent, and corresponding sides are proportional. This means that if we have two similar figures, we can conclude the following about their corresponding angles and corresponding sides:
1. Corresponding angles are congruent: The corresponding angles in similar figures have the same measure. For example, if angle A in one figure corresponds to angle A' in the other figure, then the measure of angle A is equal to the measure of angle A'.
2. Corresponding sides are proportional: The corresponding sides in similar figures are in proportion to each other. This means that the ratio of the length of one side in the first figure to the length of the corresponding side in the second figure is always the same. For example, if side AB in one figure corresponds to side A'B' in the other figure, then the ratio of AB to A'B' is constant.
To determine whether two figures are similar, we can use different strategies depending on the information we have:
1. Angle-Angle (AA) Similarity: If we know that two pairs of corresponding angles in the figures are congruent, then we can conclude that the figures are similar.
2. Side-Side-Side (SSS) Similarity: If we know that the lengths of all corresponding sides in the figures are in proportion, then we can conclude that the figures are similar.
3. Side-Angle-Side (SAS) Similarity: If we know that the lengths of two corresponding sides are in proportion, and the measures of the included angles between those sides are congruent, then we can conclude that the figures are similar.
By using these methods of comparing angles and sides, we can determine the similarity between two figures and establish the properties of corresponding angles and sides in similar figures.