Identifying Polygons in Geometry

Questions and Answers

A three-dimensional shape with curved surfaces

A figure in two-dimensional space with a finite number of straight lines (correct)

A shape with no angles or vertices

A figure with an infinite number of curved lines

All sides have different lengths

All sides have equal lengths (correct)

Some sides have equal lengths

The length of the sides are unknown

Correspondence ratio

Proportionality constant

Scale factor (correct)

Similarity coefficient

A circle is not made up of a finite number of straight lines Signup and view all the answers

By comparing either angle measures or side lengths Signup and view all the answers

They have the same measure Signup and view all the answers

Two polygons with the same shape, whether or not they have the same size Signup and view all the answers

To show similarity between two triangles Signup and view all the answers

The polygons are similar Signup and view all the answers

90 degrees Signup and view all the answers

Study Notes

A polygon is a 2D figure consisting of a finite number of straight lines that are closed, meaning a pencil can start and end at the same spot without touching a point more than once.
Examples of polygons include triangles, quadrilaterals (squares, rectangles), and octagons.
Polygons do not have to have sides of equal lengths, but if a polygon has all angles with equal measure and all sides with equal length, it is called a regular polygon.
A polygon consists of sides and vertices, where a vertex is where two sides meet, creating an angle.

Similar polygons are two polygons that have the same shape, regardless of size.
If a polygon is copied and enlarged or reduced, the new polygon and the original are similar.
Two similar polygons that are the same size are congruent polygons.

The sides of similar polygons are proportional.
The common ratio of the lengths of corresponding sides is called the scale factor.

If a correspondence can be found between pairs of angles or sides that are equal or proportional, then the polygons are similar.
There are two tests to show similarity: using angle measure and using side length proportionality.
The SAS similarity property states that if two sets of corresponding sides can be found to be proportional to one another, and the angles between these two sets of sides are equal in measure, then the two triangles are similar.

If two polygons are similar, corresponding sides are proportional and corresponding angles are equal in measure.
Examples show how to apply the concepts of similar polygons to solve problems.