Which pairs of polygons are similar…

Mathematics Questions

Which pairs of polygons are similar? Select all correct answers.

Short Answer

The rectangle and the first two triangles are similar due to equal angles and proportional sides, indicating they maintain the same shape despite size differences. Other figures, like quadrilaterals and right triangles, do not share this similarity.

Step-by-Step Solution

Rectangle and first two triangles are similar.

Step 1: Identifying Similar Polygons

To determine if two polygons are similar, we need to check if they have the same shape regardless of their size. This means that corresponding angles should be equal and the ratios of corresponding sides should be the same. For instance, observe the figures provided: identify the pairs of polygons and analyze their dimensions and angles.

Step 2: Comparing Shapes

In the given figures, look closely at the shapes of the triangles and rectangles. You will find that the first two triangles and the rectangle maintain the same outline and angle measurements despite differences in size. Note the following:

  • Triangles have equal angles and proportional sides.
  • Rectangles also display parallel sides, indicating similar properties.

Step 3: Conclusion on Similarity

After analyzing the angles and sides, we conclude that the rectangle and the first two triangles are indeed similar. Other figures, such as the quadrilaterals and right triangles, do not conform to the same criteria of similarity, as their shapes differ significantly. Thus, summarizing:

  • Rectangles and triangles maintain similarity through equal angles.
  • All corresponding sides maintain a consistent ratio.

Related Concepts

Similar polygons

Polygons that have the same shape regardless of their size, with corresponding angles equal and the ratios of corresponding sides being the same.

Similarity

The property that two shapes share when they have the same form but may differ in size, characterized by equal angles and proportional corresponding sides.

Proportional sides

The condition where the lengths of corresponding sides of two similar figures have a constant ratio, which is essential for determining similarity in geometric shapes.

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