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# Midterm

### Geometry

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

Acronym for points of concurrency. | Peanut butter cookies are best in milk chocolate and oreos. |

The point where the medians are concurrent. | Centroid. |

The point where the altitudes are concurrent. | Orthocenter. |

The point where the angle bisectors are concurrent. | Incenter. |

The point where the perpendicular bisectors are concurrent. | Circumcenter. |

The ___________ and ___________ are always concurrent inside the triangle. | Centroid, incenter. |

The ______________ and ______________ may be concurrent inside or outside the triangle. | Orthocenter, circumcenter. |

The centroid divides every median into segments with a ratio of -:-. | 2, 1. |

The orthocenter of a triangle can occur outside the triangle if the triangle is _________________. | Obtuse. |

The length of a mid segment of a triangle is __________ the length of the side of the triangle that it is parallel to. | Half. |

Shadow method formula. | Shadow/leg = leg/entire shadow |

Steps to copy an angle. | 1. Draw line longer than the first 2. Create arc from original vertex 3. Create same arc on new line 4. Measure distance of intersections from the original angle 5. Copy this distance from intersection of the 2nd line 6. Draw line through point |

Steps to create a perpendicular line through a point off a line. | 1. Draw an arc from the point so it intersects the line twice 2. Create a perpendicular bisector of the intersections 3. Connect the perpendicular bisector's intersections, which should pass through the point |

Steps to construct a square inscribed in a circle. | 1. Draw a diameter of the circle 2. Find the perpendicular bisector of the diameter 3. Connect where the perpendicular bisector intersects with the circle |

Properties of a trapezoid. | One set of parallel sides. |

Properties of a parallelogram. | Opposite sides are parallel, opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary, diagonals bisect each other, diagonal creates two congruent triangles . |

Properties of a rectangle. | Is a parallelogram, has four right angles, diagonals are congruent. |

Properties of a rhombus. | Is a parallelogram, has four equal sides, diagonals are perpendicular, diagonals bisect the angles. |

Properties of a square. | Is a parallelogram, rectangle, and a rhombus. |

Properties of an isosceles trapezoid. | Has one set of parallel sides, the sides that are not parallel are congruent, base angles are congruent, diagonals are congruent, opposite angles are supplementary. |

Sides of a 45-45-90 triangle. | x, x, x radical 2. |

Sides of a 30-60-90 triangle. | x, x radical 3, 2x. |

Polygon with seven sides. | Heptagon/Septagon. |

Polygon with nine sides. | Nonagon. |

Polygon with ten sides. | Decagon. |

Polygon with eleven sides. | Hendecagon. |

Polygon with twelve sides. | Dodecagon. |

In two similar polygons, the ratio of the perimeters is __________ to the ratio of the sides. | Equal. |

Angle Bisector Theorem. | Leg Half of the opposite side of the bisected angle ________ = ___________________________ Both legs Entire bisected side |

Steps to construct a perpendicular line through a point on a line. | 1. Draw arc from point on line 2. Draw same size arc on other side of the point 3. Draw larger arc from intersection from 1st arc 4. Draw same size arc from intersection of 2nd arc 5. Repeat steps 3/4 on opposite side 6. Connect intersections |

Steps to bisect an angle. | 1. Draw an arc from the vertex 2. Draw the same size arc from the intersections of the original arc 3. Connect the vertex to the new intersection |

Steps to construct a translation. | 1. Measure line of translation 2. Keep compass size and draw circle around end points 3. Measure from arrow to endpoint 4. Keep size and draw arc from end point of translation 5. Repeat steps 3 and 4 for other end 6. Connect arcs' intersections |

Steps to construct an equilateral triangle inscribed in a triangle. | 1. Draw an arc on the circle 2. Keep the compass size and continue to draw arcs that are the same distance apart 3. Connect three arcs that are not next to each other |

Steps to construct a square. | 1. Extend line given line 2. Draw a small arc on both sides of a point 3. Create a perpendicular bisector of the two arcs 4. Repeat steps 2 and 3 for other point 5. Measure given line 6. Create an arc that size from points 7. Connect points |

Steps to construct an altitude of a triangle. | 1. Draw arc from vertex that intersects opposite line twice 2. Change size to 3/4 of distance between two intersections and draw arc between one intersection and vertex 3. Repeat step 2 for other intersection 4. Connect vertex with new intersection |

Steps to construct a parallel line. | 1. Measure from point not on line to midpoint of line and draw a semicircle 2. Measure between point and end of line and draw arc from opposite side of line 3. Connect point to intersection |