2. Course: Applied Geo. Aim: Similarity Aim: What are Similar Polygons? What is a Scale Factor or Ratio of Similitude? Do Now: What is ratio of the length of picture A to the length of picture B Big Sara smiles Little Sara smiles The lengths and widths of the pictures are in the same ratio. Similar - corresponding, comparable, alike ~ ~ Download Sketch 48 and fill in the accompanying worksheet.

3. Course: Applied Geo. Aim: Similarity Aim: What are Similar Polygons? What is a Scale Factor or Ratio of Similitude? Do Now: What is ratio of the length of picture A to the length of picture B 10” 5” 2” 4” Similarly, find the ratio of the width of picture A with the width of picture B A B The lengths and widths of the pictures are in the same ratio. Similar - corresponding, comparable, alike ~ ~

4. Course: Applied Geo. Aim: Similarity Ratio compares 2 numbers by division the ratio 1 to 4 is written 1 : 4 or 1/4 the ratio 4 : 1 is not the same as 1 : 4 Reduce a ratio: divide numerator and denominator by greatest common factor Ex. other ratios equal to 1/4 are found by multiplying numerator and denominator by the same factor Ex.

5. Course: Applied Geo. Aim: Similarity

6. Course: Applied Geo. Aim: Similarity A B 55 54 44 5 5 No Yes Can you say either pair of polygons is similar to each other? AD SV = AB CD ST UV DC VU = AB CD ST UV Are dimensions of corresponding parts for polygons in column A & column B in the same ratio? AD SV = DC VU = HOW DO THE TWO PAIRS COMPARE? 4 3

7. Course: Applied Geo. Aim: Similarity How do we define precisely what are properties of similar figures? Are corresponding parts congruent? Are corresponding angles congruent? Do the shapes look alike? Can they look different? Explain what you think is meant by similar geometric shapes. What does similar mean? What does similarity mean in geometry?

8. Course: Applied Geo. Aim: Similarity 1. Similar polygons are two polygons in which the A) corresponding sides are in proportion and the B) corresponding angles are congruent. scale factor ratio of similitude The scale factor comparing two corresponding sides of similar polygons is also called the ratio of similitude A) Corresponding sides are in proportion B) Corresponding angles are congruent Ratio of Similitude Note: Similar Polygons have the same shape, but are of different size

9. Course: Applied Geo. Aim: Similarity What is the ratio of similitude for these figures? Quadrilateral 1 ~ Quadrilateral 2. Find the value of the variables. 6 4 x y z 15 12 9 Recall: All corresponding sides of similar polygons are in proportion: the ratio of similitude or scale factor y = 8x = 6z = 10 1 2