Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

Normal Size Small Size show me how

Normal Size Small Size show me how

# Mathematics 217

### Chapters 13 - 14

Term | Definition |
---|---|

Isometry | Any rigid motion that preserves length or distance is an isometry. It can be shown that under any isometry, the image of a line is a line, the image of a circle is a circle, and the images of parallel lines are parallel lines. |

Translation | A translation is a motion of a plane that moves every point of the plane a specified distance in a specified direction along a straight line. |

Translation in a coordinate system | A translation is a function from the plane to the plane such that to every point (x,y) corresponds the point (x + a, y + b), where a and b are real numbers. |

Rotation | A rotation is a transformation of the plane determined by holding one point, the center, fixed and rotating the plane about this point by a certain amount in a certain direction. |

Special rotation | A rotation of 360° about a point moves any point and hence any figure onto itself. Such a transformation is an identity transformation. Any point may be the center of such a rotation. A rotation of 180° about a point is a half-turn. |

Slopes of perpendicular lines | We can use transformations to investigate various mathematical relationships, including the slopes between two non-vertical perpendicular lines. If we rotate a line in the plane by 90 degrees about a point on the line, we have a perpendicular line. |

Reflection | A reflection in a line ℓ is a transformation of a plane that pairs each point P of the plane with a point P′ in such a way that ℓ is the perpendicular bisector of PP′, as long as P is not on ℓ. |

Glide reflection | Glide reflection, is a transformation consisting of a translation followed by a reflection in a line parallel to the slide arrow. |

Areas on a geoboard (dot paper) | Addition method divide an area into smaller pieces and then add the areas. |

Areas of a geoboard (dot paper) | Rectangle method is to construct a rectangle encompassing the entire figure and then subtract the areas of the unshaded regions. |

Pythagorean theorem | Given a right triangle with legs a and b and hypotenuse c, c2 = a2 + b2. |

45 degrees 45 degrees 90 degrees right triangle | The length of the hypotenuse in a 45°-45°-90° (isosceles) right triangle is the square root of 2 times the length of a leg. |

30 degrees 60 degrees 90 degrees right triangle | In a 30°-60°-90° right triangle, the length of the hypotenuse is twice the length of the leg opposite the 30° angle (the shorter leg). |

Created by:
marianhood