WMHS Proportionality Theorems

Similarity Transformation

Triangle Proportionality Theorem

If a line is parallel to one side of a triangle, & it intersects two sides into two distinct points, then it separates these sides into segments of proportional lengths.

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Find the width of the river

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Angle Bisector Theorem

If a ray bisects an angle of a triangle, then it divides the opposite side proportional to the other two sides.

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How do you dilate the line segment on the graph centered at a point on the line segment?

Use (2, 4) as the center of dilation. If k = 2, what are the new coordinates?

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How do you dilate the line segment on the graph centered at the origin?

Use (2, 4) as the center of dilation. If k = 2, what are the new coordinates?

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When dilating a line that does not pass through the center of dilation, the dilated line is parallel to the original.

(x, y) --> (kx, ky) changes the size of the figure by a factor of k when the center of dilation is the origin.

Use (3, 6) as the center of dilation.

If k = 4, what are the new coordinates?

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In Conclusion:

A dilation produces an image in the same shape as the original but is a different size.

When dilating a line segment, the dilated line segment is longer or shorter with respect to the scale factor.