Key Concepts:
1. Similar figures are figures that have the same shape but not necessarily the same size. To determine if two figures are similar, you can check if their corresponding angles are congruent and their corresponding sides are proportional.
2. When two figures are similar, you can create one figure from the other through transformations such as dilation, rotation, reflection, and translation.
3. Dilation is a transformation that enlarges or reduces a figure by a scale factor. The scale factor is used to determine how much larger or smaller the figure becomes.
4. Rotations are transformations that turn a figure around a fixed point called the center of rotation. The angle of rotation determines how much the figure is rotated.
5. Reflections are transformations that flip a figure over a line called the line of reflection. The figure is a mirror image of its original shape.
6. Translation is a transformation that slides a figure in a certain direction without changing its size or shape.
7. Similar figures have corresponding angles that are congruent and corresponding sides that are proportional. This means you can set up proportions to find missing side lengths in similar figures.
Examples:
1. Determine if the following shapes are similar:
Shape 1:
- Corresponding angles: ∠A is congruent to ∠D, ∠B is congruent to ∠E, ∠C is congruent to ∠F
- Corresponding sides: AB/DE = BC/EF = AC/DF
Since the corresponding angles are congruent and the corresponding sides are proportional, Shape 1 and Shape 2 are similar.
2. Given two similar triangles ABC and DEF, where AB = 6, BC = 8, and DE = 9, find the length of EF.
Since the triangles are similar, you can set up a proportion to find the missing side length:
AB/DE = BC/EF
6/9 = 8/EF
Cross multiply:
6EF = 72
EF = 12
So, the length of EF is 12.
UNIT 3 LESSON 3 Transformations and Similarity Similar Figures
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