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Questions and Answers
What is a polygon?
What is a polygon?
What is true about the sides of a regular polygon?
What is true about the sides of a regular polygon?
What is the common ratio of the lengths of corresponding sides in similar triangles called?
What is the common ratio of the lengths of corresponding sides in similar triangles called?
What is the main difference between a polygon and a circle?
What is the main difference between a polygon and a circle?
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Which method can be used to show similarity between two polygons?
Which method can be used to show similarity between two polygons?
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What is true about the corresponding angles of similar polygons?
What is true about the corresponding angles of similar polygons?
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What is the definition of similar polygons?
What is the definition of similar polygons?
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What is the SAS similarity property used for?
What is the SAS similarity property used for?
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What can be concluded if a correspondence can be found between pairs of angles in two polygons, where the corresponding angles are equal?
What can be concluded if a correspondence can be found between pairs of angles in two polygons, where the corresponding angles are equal?
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What is the missing angle measure in Hexagon 2 in Example 2?
What is the missing angle measure in Hexagon 2 in Example 2?
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Study Notes
What are Polygons?
- 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.
What are Similar Polygons?
- 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.
Angles of Similar Polygons
- Corresponding angles of similar polygons are equal in measure.
Sides of Similar Polygons
- The sides of similar polygons are proportional.
- The common ratio of the lengths of corresponding sides is called the scale factor.
How to Tell If Polygons are Similar
- 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.
Similar Polygons Examples
- 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.
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Description
Learn about polygons, a type of 2D shape composed of straight lines, including triangles, quadrilaterals, and octagons. Understand the properties of polygons and how to identify them.
