Slope and similar triangles

Guiding Questions What is true about corresponding sides of similar triangles? How does the slope of two similar triangles compare?

Similar Figures Similar figures have exactly the same shape but not necessarily the same size. Corresponding sides of two figures are in the same relative position, and corresponding angles are in the same relative position. Two figures are similar if and only if the lengths of corresponding sides are proportional and all pairs of corresponding angles have equal measures.

The ratios of the rise to the run of the two similar slope triangles are the same as the slope of the line. Since the ratios are equal, the slope of m of a line is the same between any two distinct points on a non-vertical line in the coordinate plane.

a rise run 4 2 2 1 6 2 b c rise run 6 3 2 1 3 4 1 d e be de ac bc 4 2 Write a proportion to compare the rise to the run for each of the similar slope triangles Y a Triangle # 1 rise run 4 2 2 1 6 2 b Triangle # 2 c rise run 6 3 2 1 3 X 4 1 d proportion e be de ac bc 4 2 6 3 2 1 2 = = =

Pick 2 points on the line and find the slope Y (x2, y2) (12,8) rise run Slope formula y2 – y1 x2 – x1 1 2 (8,6) (x2, y2) (x1, y1) (2,3) 3 – 2 2 - 0 1 2 Pick 2 different points on the line and find the slope of those points (0,2) (x1, y1) X rise run Slope formula y2 – y1 x2 – x1 2 4 1 2 8 – 6 12 - 8 2 4 1 2

Guiding Questions (you should be able to answer) What is true about corresponding sides of similar triangles? How does the slope of two similar triangles compare?