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# S & S

### CMP2 Stretching and Shrinking: similar figures

Question | Answer |
---|---|

The number that you multiply the sides in a figure by to create a similar figure. | Scale Factor |

When two shapes have equal corresponding angles and the corresponding sides have been multiplied by the same number. | similar figures |

When two shapes are exactly the same. | congruent |

(3x, 4y) (6x, 6y) and (x+1, 3y-2) are all examples of what? | algebraic rules |

Will the rule (6x, 6y) make a similar figure? | yes (the sides and perimeter will be six times larger, the angles stay the same, the area will be 36 times larger) |

Will the rule (6x, 2y) make a similar figure? | no (the height is 2 times larger but width is 6 times larger) |

Compare angles, side lengths, perimeters and areas if a copy is made using a copier factor of 300%. | Sides and perimeter are 3 times larger, angles are congruent, and the area would be 9 times larger. |

In similar figures how do side lengths and perimeters compare? | They multiply by the same factor. |

If the scale factor from the original shape to a larger shape is 7 then how do the areas compare. | The area of the original times 49 would equal the area of the enlargement. The area of the enlargement times 1/49 would equal the area of the original. |

What rule would make a figure with side lengths one fifth the length of the original? | (1/5x, 1/5y) |

Compare angles, side lengths, perimeters and areas if a copy is made using a copier factor of 20%. | Sides and perimeter are .20 times smaller, angles are congruent, and the area would be .04 times smaller. |

The scale factor from figure A to figure B is k. What is the scale factor from figure B to figure A? | 1/k |

The scale factor from figure A to figure B is k. How does the area of figure A compare to the area of figure B? | The area of figure A times k squared would give the area of figure B. |

What happens to a figure if you add to the x-coordinate? | It will move right. |

What happens to a figure if you subtract from the x-coordinate? | It will move left. |

What happens to a figure if you add to the y-coordinate? | It will move up. |

What happens to a figure if you subtract from the y-coordinate? | It will move down. |

How do you make a reduction? | You multiply by a number between 0 and 1. |

What must you always do when comparing with scale factor? | You must be specific about which direction you are working (is big to small k=1/3 or small to big k=3). |

What 5 properties should you compare when shapes are similar? | Side lengths, perimeter(s), angles, area(s), and position |

How would an original shape compare to a new shape which was created using the rule (5x-1, 5y+3)? | The side lengths of the new shape are 5 times longer than the original, the angles are congruent, the perimeter is also 5 times larger, the area would be 25 times larger, and the new shape would be moved to the left 1 and up 3. |

If small to big k=10 then how do the area(s) compare? | The big area(s) are 100 times larger. |

If small to big k=10 then how do the perimeter(s) compare? | The big P is 10 times larger than the small P. |

Will the rule (6x+7, 2y+7) make a similar figure? | No, x and y are multiplied by different numbers. |

Will the rule (6x+7, 6y+89) make a similar figure? | Yes, x and y are multiplied by the same number. |

If a 3 in by 4 in picture is enlarged by a copier factor of 400% what would the new length be? | 16 in |

If a 3 in by 4 in picture is reduced by a copier factor of 25% what would the new length be? | 1 in |

What two things do you need to compare when looking for similar figures? | corresponding sides and corresponding angles |

If two figures have equivalent ratios of corresponding sides can you be certain that those figures are similar? | No, they must also have congruent corresponding angles. |

What must you do when asked to write a ratio? | Tell which sides you are using (ie short to long vs long to short) |

If two figures are similar what will be true about their ratios of corresponding sides? | They will be equivalent ratios. |

What are the three ways that you can write a ratio? | With the word "to", with a :, and using the fraction bar. |

What is a ratio? | A ratio is a comparison of TWO numbers. |

Created by:
rratclif