By CK-12 Foundation

CK-12’s Geometry - moment variation is a transparent presentation of the necessities of geometry for the highschool pupil. subject matters comprise: Proofs, Triangles, Quadrilaterals, Similarity, Perimeter & zone, quantity, and variations. quantity 2 contains the final 6 chapters: Similarity, correct Triangle Trigonometry, Circles, Perimeter and zone, floor sector and quantity, and inflexible ameliorations.

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**Additional resources for CK-12 Geometry - Second Edition, Volume 2 of 2**

**Example text**

Are the two diamonds similar? If so, what is the scale factor? Explain your answer. Similar Polygons Similar Polygons: Two polygons with the same shape, but not the same size. Think about similar polygons as an enlargement or shrinking of the same shape. So, more specifically, similar polygons have to have the same number of sides, the corresponding angles are congruent, and the corresponding sides are proportional. The symbol is used to represent similar. Here are some examples: These polygons are not similar: Example 1: Suppose .

Solution: First, draw the altitude from the vertex between the congruent sides, which will bisect the base (Isosceles Triangle Theorem). Then, find the length of the altitude using the Pythagorean Theorem. Now, use and in the formula for the area of a triangle. The Distance Formula Another application of the Pythagorean Theorem is the Distance Formula. We have already been using the Distance Formula in this text, but we can prove it here. First, draw the vertical and horizontal lengths to make a right triangle.

Corollary 7-3: If and are nonzero and , then . In other words, a true proportion is also true if you switch the means, switch the extremes, or flip it upside down. Notice that you will still end up with after cross-multiplying for all three of these corollaries. Example 6: Suppose we have the proportion . Write down the other three true proportions that follow from this one. Solution: First of all, we know this is a true proportion because you would multiply by to get . Using the three corollaries, we would get: If you cross-multiply all four of these proportions, you would get for each one.