Using similar polygons

I remember vividly as an adolescent, I got thrilled and psyched seeing action and sci-fi movies especially those involving large guns and grenades, using similar polygons. The first day I ever heard the word 'polygon' in the class, as introduced by my Maths teacher, Mr. Finicky Spins, I was so elated. Do you know why?

As you may recall, congruent polygons have the exact same size and are a perfect match because all corresponding parts are congruent equal. Whereas, similar polygons have the same shape, but not the same size i. This means that if two polygons are similar, then their corresponding angles are congruent but their their corresponding sides are proportional as displayed in the figure below. Remember, a ratio is a fraction comparing two quantities, and a proportion is when we set two ratios equal to each other. And we can use cross multiplication to solve a proportion. If two polygons are similar, then the ratio of the lengths of any two corresponding sides is called the scale factor.

Using similar polygons

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How do you identify similar polygons? Load, aim, and shoot 'polyguns'.

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A circle, cube, or oval is not a polygon. A triangle is a polygon. The capital letter L is not a polygon. Similar polygons involve two mathematical concepts similarity and polygons , and have within them an additional concept, proportion. First look at the angles. Are they the same from one triangle to the other? They are not. Look at the lengths of their sides. An equilateral triangle is not proportionally the same as a right triangle.

Using similar polygons

As you may recall, congruent polygons have the exact same size and are a perfect match because all corresponding parts are congruent equal. Whereas, similar polygons have the same shape, but not the same size i. This means that if two polygons are similar, then their corresponding angles are congruent but their their corresponding sides are proportional as displayed in the figure below. Remember, a ratio is a fraction comparing two quantities, and a proportion is when we set two ratios equal to each other. And we can use cross multiplication to solve a proportion. If two polygons are similar, then the ratio of the lengths of any two corresponding sides is called the scale factor. This means that the ratio of all parts of a polygon is the same as the ratio of the sides. For example, using the figure above, the simplified ratio of the lengths of the corresponding sides of the similar trapezoids is the scale factor.

Fridans

How to solve a similar polygon? This question refers again to figure 1. This means that the ratios of these pairs are equal:. Their lengths are directly proportional. Non-necessary Non-necessary. When making diagrams for similar polygons, careful attention must be given to the labeling of the vertices and the ordering of these labels. How would you like to learn this content? Step 3: Find the area of the smaller triangle cut out. What is a polygon? But you would need to know the ratio between both angles. The techniques above can be used together to find other properties of polygons such as their height, perimeter, and area.

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Register for Free I'll do it later. Key takeaways - Using Similar Polygons Two polygons are similar if they have the same number of sides and their corresponding angles are equal. Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. Their vertices can be paired up so that the corresponding sides have lengths that are in proportion, and all of the pairs of corresponding angles are equal. What two conditions are needed for two polygons to be similar? The techniques above can be used together to find other properties of polygons such as their height, perimeter, and area. Sign up now for free. It is mandatory to procure user consent prior to running these cookies on your website. Explore our app and discover over 50 million learning materials for free. This can still be solved if all of the sides are in terms of the same unknown quantity. Taking a short quiz. Start Quiz. Interpret the question word for word from the first sentence to the next.