Two corresponding sides of two similar hexagons are 16 mm and 20 mm.
What is the ratio of the area of the two hexagons?
Name the postulate and two theorems you can use to prove triangle similarity.
ratio of areas of similar figures is ratio of corresponding lengths squared
20/16 = 5/4 so 25/16
Thanks, what about
Name the postulate and two theorems you can use to prove triangle similarity.
Thank you
http://www.regentsprep.org/Regents/math/geometry/GP11/LsimilarProof.htm
https://www.khanacademy.org/math/geometry/similarity/triangle_similarlity/v/similarity-postulates
Thank you Damon
You are welcome.
To find the ratio of the area of two hexagons, we need to know the ratio of the lengths of their corresponding sides. In this case, we are given that two corresponding sides of the two hexagons are 16 mm and 20 mm.
To find the ratio of the area, we need to calculate the ratio of the squares of the corresponding side lengths, as the area of a polygon is proportional to the square of its side length.
Let's calculate the ratio of the squares of the corresponding side lengths:
Ratio = (20 mm)^2 / (16 mm)^2 = 400 / 256 = 1.5625
Therefore, the ratio of the area of the two hexagons is approximately 1.5625.
Regarding the second part of your question, there are several postulates and theorems you can use to prove triangle similarity. Here are three commonly used ones:
1. Side-Side-Side (SSS) Similarity Postulate: If the corresponding sides of two triangles are proportional, then the triangles are similar.
2. Angle-Angle (AA) Similarity Theorem: If two corresponding angles of two triangles are congruent, then the triangles are similar.
3. Side-Angle-Side (SAS) Similarity Theorem: If the ratio of the lengths of two corresponding sides of two triangles is proportional, and the included angle between those sides is congruent, then the triangles are similar.
These postulates and theorems can be used to determine if two triangles are similar or to prove the similarity of triangles in geometric proofs.