Mathematics Exam > Mathematics Notes > Additional Topics for IIT JAM Mathematics > Similarity between Triangles and Polygons
Similarity between Triangles and Polygons | Additional Topics for IIT JAM Mathematics PDF Download
Polygons
Any two polygons are similar if their corresponding angles are congruent and the measures of their corresponding sides are proportional:
In the figure above the ratio or the scale factor of the quadrilateral to the left versus the quadrilateral to the right is ½. We could also turn it around and say that the scale factor for the quadrilateral to the right to the quadrilateral to the left is 2.
Triangles
If the measures of the corresponding sides of two triangles are proportional then the triangles are similar. Likewise if the measures of two sides in one triangle are proportional to the corresponding sides in another triangle and the including angles are congruent then the triangles are similar.
If a line is drawn in a triangle so that it is parallel to one of the sides and it intersects the other two sides then the segments are of proportional lengths:
Parts of two triangles can be proportional; if two triangles are known to be similar then the perimeters are proportional to the measures of corresponding sides.
Continuing, if two triangles are known to be similar then the measures of the corresponding altitudes are proportional to the corresponding sides.
Lastly, if two triangles are known to be similar then the measures of the corresponding angle bisectors or the corresponding medians are proportional to the measures of the corresponding sides.
The bisector of an angle in a triangle separates the opposite side into two segments that have the same ratio as the other two sides:
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FAQs on Similarity between Triangles and Polygons - Additional Topics for IIT JAM Mathematics
| 1. What is the difference between a triangle and a polygon? |  |
Ans. A triangle is a type of polygon that has three sides and three angles. A polygon, on the other hand, is a closed figure with straight sides and angles. So, while all triangles are polygons, not all polygons are triangles.
| 2. Can a triangle be considered a polygon? | |
Ans. Yes, a triangle is a type of polygon. A polygon is a closed figure with straight sides and angles, and a triangle fits this definition as it has three sides and three angles.
| 3. Are all polygons made up of triangles? | |
Ans. No, not all polygons are made up of triangles. Polygons can have any number of sides, and while triangles are polygons, polygons can also have more than three sides. For example, a square or a pentagon are polygons that are not made up of triangles.
| 4. What are some properties of triangles and polygons? | |
Ans. Triangles have unique properties such as the sum of their interior angles being equal to 180 degrees, and the sum of any two sides being greater than the third side. Polygons, in general, have properties related to the number of sides, angles, and symmetry. For example, the sum of the interior angles of an n-sided polygon is given by (n-2) * 180 degrees.
| 5. How are triangles and polygons used in real-world applications? | |
Ans. Triangles and polygons have numerous real-world applications. In architecture and construction, they are used to design and create structures with specific shapes and angles. In computer graphics and animation, polygons are used to create 3D models and render realistic images. Triangles are also used in surveying and GPS systems to calculate distances and locations accurately.
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