Add to your notes Corollaries If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally. If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

Agenda Homework Review Parts of Similar Triangles Fractals Homework Flatland – 0 to 3 dimensions – Euclidean Geometry Edwin A Abbott – Headmaster 1884 Flatterland – Euclidean & Non-Euclidean, Physics Ian Stewart 2001

7-4 Study Guide

7-4 Practice

7-4 Practice

7-4 Practice

Parts of Similar Triangles Proportional Perimeters Theorem If two triangles are similar, then the perimeters are proportional to the measures of corresponding sides.

Example If LMN ~ QRS, QR = 40, RS = 41, SQ = 9 and LM = 9, find the perimeter of LMN.

Example

Theorem If two triangles are similar, then the measures of the corresponding altitudes are proportional to the measures of the corresponding sides. BG AB ---- = ---- EH DE BG BC ---- = ---- EH EF

Theorem If two triangles are similar, then the measures of the corresponding angle bisectors of the triangles are proportional to the measures of the corresponding sides. TA RT ---- = ---- GB EG

Theorem If two triangles are similar, then the measures of the corresponding medians are proportional to the measures of the corresponding sides.

Theorem Angle Bisector Theorem An angle bisector in a triangle separates the opposite side into segments that have the same ratio as the other two sides. C AD AC ---- = ---- DB BC B A D

7-6 Fractals and Self-Similarity Iteration A process of repeating the same procedure over and over. Fractal A geometric figure that is created using iteration. Self-Similar Smaller and smaller details of a shape have the same geometric characteristic as the original, larger form. Strictly Self-Similar All parts, no matter where they are located or no matter what size is selected, contain the same geometric figure as the whole.

Sierpinski’s Triangle stage ?

Koch’s Curve Stage 0 Stage 1 Stage 2 Stage 3

Koch’s Curve

Answers Ahead

7-5 Study Guide

7-5 Practice

7-5 Practice

7-5 Practice

7-5 Practice

Homework 7-5 Study Guide & Practice 7-6 Study Guide & Practice