tell whether the pair of polygons are similar explain why or why not
To determine if a pair of polygons is similar, you need to examine their corresponding angles and side lengths. Two polygons are considered similar if their corresponding angles are congruent and their corresponding sides are in proportion.
Here’s how you can determine whether a pair of polygons is similar:
1. Identify the corresponding angles: Start by identifying the corresponding angles between the two polygons. If all corresponding angles are congruent, it is a good indication that the polygons are similar.
2. Measure the corresponding side lengths: Measure the lengths of the corresponding sides of the polygons. If the ratio of the lengths between the corresponding sides is equal, then the polygons are similar. You can find the ratio by dividing the length of a side in one polygon by the length of the corresponding side in the other polygon.
For example, if you have two triangles with corresponding sides of lengths 4 cm and 8 cm, you divide the longer side by the shorter side: 8 cm ÷ 4 cm = 2. If the ratio is the same for all corresponding sides, then the polygons are similar.
3. Apply the SSS, SAS, or AA similarity theorem: If you are dealing with triangles, you can apply the SSS (Side-Side-Side) or SAS (Side-Angle-Side) similarity theorem to determine similarity. According to the SSS theorem, if the ratios of corresponding side lengths are equal, the triangles are similar. According to the SAS theorem, if the ratios of two pairs of corresponding sides and the included angles are equal, the triangles are similar.
4. Consider additional properties: Sometimes, polygons may appear similar due to a common shape, like squares, rectangles, or pentagons. However, being the same shape does not guarantee similarity unless the corresponding angles and side lengths also match.
By following these steps and considering the corresponding angles and side lengths, you can determine whether a pair of polygons is similar or not.