Chapter 7: Proportions and Similarities
Resources
Challenge Question by Ishwari
Find x.
*The answer is below. If you need steps for the question, you can message me.*
7.1-7.4 Mid-Chapter Quiz Answer Key
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Chapter 7 Textbook Reviews
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7.1 - Ratios & Proportions
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Worksheet #1 (Includes Answers)
7.2 - Similar Polygons
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Worksheet #3 (Recommended)
7.3 - Similar Triangles
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Kuta Worksheet #1 (Recommended)
Khan Academy Practice (Recommended)
Workshseet #2 (Answer Key Provided)
7.4 - Parallel Lines and Proportional Parts
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Kuta Worksheet #2 (Advanced)
Challenge Problem (Extreme Advanced)
*Note: This type of problem won't be seen on the quiz. Guaranteed by Mr.Himmelstein*
7.5 - Parts of a Similar Triangle
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Textbook Problems and Solutions I was unable to find many worksheets, so just use worksheets from the textbook
7.6 - Similarity Transformations
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Worksheet #1 I was unable to find many worksheets, so just use worksheets from the textbook
7.7 - Scale Drawings and Models
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Resources
7.1 - Ratios & Proportions
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~ Ratio is a comparison of 2 quantities using division. It can be expressed in 3 different ways. 3 to 4, 3/4, 3:4
~ Proportion is an equation stating 2 or more ratios are equal.
~ 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
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~ 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
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~ 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
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~ 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.
7.5 - 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) .