Warm Up

DILATIONS, SIMILAR FIGURES, & PROVING FIGURES SIMILAR Tuesday October 29 th

On graph paper  Plot Triangle RST with endpoints on gridlines  Plot triangle RST on a second graph-same coordinates  Predict what will happen to the figure if we multiply by a number. (instead of adding or subtracting)  What will happen if we multiply by a number LARGER than 1?  What will happen if we multiply by a number BETWEEN 0 and 1?

On graph paper  Multiply the coordinates by 2  Plot those points as R’S’T’  Multiply the original coordinates by ½  Plot those points as R’’S’’T’’  What happened in each?

Dilations  Multiply by x>1 gets bigger  Multiply 0<x<1 gets smaller  We call shapes with the same shape but different sizes________  Gets bigger = ENLARGEMENT  Gets smaller = REDUCTION  We multiply the coordinates by the SCALE FACTOR Similar

Example  Graph the coordinates S(-1, -3), U(2, 4), M(3, -2), R(-3, 4) on two graphs  ENLARGE the preimage by a scale factor of 2  Label the image S’U’M’R’  REDUCE the preimage by a scale factor of 1/3  Label the image S”U”M”R”

Find the scale factor  Solid lines = Preimage  Set up your ratio as: IMAGE / PREIMAGE

Enlargement or Reduction?

Dilations

Similar Figures Similar- same shape not necessarily the same size  Corresponding Angles are CONGRUENT  Corresponding Sides are PROPORTIONATE We write a SIMILARITY STATEMENT as ABCD ~ XYZW

Write a Similarity Statement

Scale Models  A real soccer field: 100 yds long and 60 yds wide  What are the proportions you can make using the real field? 100 yds 60 yds

Are these similar figures?  If yes, write a similarity statement and the scale factor.  If no, why not?

You Try!

Word Problem!

Find the Error

Similarity Word Problem  A 1.6-m-tall woman stands next to the Eiffel Tower. At this time of day, her shadow is 0.5 m long. At the same time, the tower’s shadow is m long. How tall is the Eiffel Tower?

If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. Proportional Lengths Theorem

If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional. Corollary to the Proportional Lengths Theorem

Solve for x in the following. Try Some

The map at the right shows the walking paths at a local park. The garden walkway is parallel to the walkway between the monument and the pond. How long is the path from the pond to the playground? Similarity Word Problem

The business district of a town is shown on the map below. Maple Avenue, Oak Avenue, and Elm Street are parallel. How long is the section of First Street from Elm Street to Maple Avenue? Similarity Word Problem

Homework  Worksheet