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# geometry midterm2011

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

Reflexive Property | A quantity is congruent (equal) to itself. a = a |

Symmetric Property | If a = b, then b = a. |

Transitive Property | If a = b and b = c, then a = c. |

Addition Postulate | If equal quantities are subtracted from equal quantities, the differences are equal. |

Subtraction Postulate | If equal quantities are subtracted from equal quantities, the differences are equal. |

Multiplication Postulate | If equal quantities are multiplied by equal quantities, the products are equal. (also Doubles of equal quantities are equal.) |

Division Postulate | If equal quantities are divided by equal nonzero quantities, the quotients are equal. (also Halves of equal quantities are equal.) |

Substitution Postulate | A quantity may be substituted for its equal in any expression. |

Partition Postulate | The whole is equal to the sum of its parts. |

Angle Addition Postulate | m |

Construction | Two points determine a straight line. |

Right Angles | All right angles are congruent. |

Straight Angles | All straight angles are congruent. |

Congruent Supplements | Supplements of the same angle, or congruent angles, are congruent. |

Congruent Complements | Complements of the same angle, or congruent angles, are congruent. |

Linear Pair | If two angles form a linear pair, they are supplementary. |

Vertical Angles | Vertical angles are congruent. |

Triangle Sum | The sum of the interior angles of a triangle is 180ยบ. |

Exterior Angle | The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. The measure of an exterior angle of a triangle is greater than either non-adjacent interior angle. |

Base Angle Theorem (Isosceles Triangle) | If two sides of a triangle are congruent, the angles opposite these sides are congruent. |

Base Angle Converse (Isosceles Triangle) | If two angles of a triangle are congruent, the sides opposite these angles are congruent. |

Side-Side-Side (SSS) Congruence | If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. |

Side-Angle-Side (SAS) Congruence | If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. |

Angle-Side-Angle (ASA) Congruence | If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. |

Angle-Angle-Side (AAS) Congruence | If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. |

Hypotenuse-Leg (HL) Congruence (right triangle) | If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent. |

CPCTC | Corresponding parts of congruent triangles are congruent. |

Angle-Angle (AA) Similarity | If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. |

SSS for Similarity | If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar. |

SAS for Similarity | If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. |

Side Proportionality | If two triangles are similar, the corresponding sides are in proportion. |

Mid-segment Theorem (also called mid-line) | The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long. |

Sum of Two Sides | The sum of the lengths of any two sides of a triangle must be greater than the third side |

Longest Side | In a triangle, the longest side is across from the largest angle. In a triangle, the largest angle is across from the longest side. |

Altitude Rule | The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. |

Leg Rule | Each leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse. |

Corresponding Angles | If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. |

Corresponding Angles Converse | If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel. |

Alternate Interior Angles | If two parallel lines are cut by a transversal, then the alternate interior angles are congruent. |

Alternate Exterior Angles | If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent. |

Interiors on Same Side | If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary. |

Alternate Interior Angles Converse | If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel. |

Alternate Exterior AnglesConverse | If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are parallel. |

Interiors on Same Side Converse | If two lines are cut by a transversal and the interior angles on the same side of the transversal are supplementary, the lines are parallel. |

geometric mean | x=square root(ab) |

30 60 90 | X, 2X, Xsquare root of 3 |

45 45 90 | square root of 2 over 2 |

vertical angles | across |

Created by:
adeleverrengia