~ Below is an image showing means and extremes. Multiplying the extremes and setting them equal to the product of means equals the cross product of a proportion.

7.2 - Similar Polygons

Thanks to Ishwari Veerkar

~ Similar Polygons have the same shape but not necessarily the same sizes.

~ The ratio of the 2 lengths of the corresponding sides of 2 similar polygons is called the scale factor. The scale factor is dependent on the order of comparison.

~ If two polygons are similar, then their perimeters are proportional to the scale factor between them.

7.3 - Similar Triangles

Thanks to Ishwari Veerkar

~ Angle Angle Similarity: If 2 angles of one triangle are congruent to 2 angles of other triangle, then the triangles are similar.

~ SSS Similarity: If the corresponding side lengths of 2 triangles are proportional then the triangles are similar.

~ SAS Similarity: If the lengths of 2 sides of a triangles are proportional to the lengths of the 2 corresponding sides of a triangle and the included angles are congruent then the triangles are similar.

7.4 - Parallel Lines and Proportional Parts

Thanks to Ishwari Veerkar

~ Angle Angle Similarity: If 2 angles of one triangle are congruent to 2 angles of other triangle, then the triangles are similar.

~ SSS Similarity: If the corresponding side lengths of 2 triangles are proportional then the triangles are similar.

7.5 - Parts of a Similar Triangle

Thanks to Nidhi

The medians, altitudes, and angle bisectors of two similar triangles have the same scale factor as the sides of the triangles. The ratio of the two segments formed by the intersection of an angle bisector is equivalent to the ratio formed by the other two sides.

7.6 - Similarity Transformations

Thanks to Ishwari Veerkar

A dilation is a transformation that enlarges or reduces the preimage proportionally.

For a dilation to be an enlargement the scale factor or the k > 1

For a dilation to be a reduction the scale factor or the k, 0 < k < 1

7.7 - Scale Drawings and Models

There aren't any notes required for this lesson. Just solve the examples from the textbook or from the worksheets above.

Challenge Question

The answer is 51 degrees.

If you need a better understanding of the question feel free to private message me (Ishwari Veerkar) .

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