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# Thm Chap 2-7

### Theorems from Chapters 2-7

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

All right angles are congruent | Right Angles Congruence Theorem |

If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is an acute triangle | Pythagorean Acute Triangle Theorem |

The sum of the lengths of any two sides of a triangle is greater than the length of the third side | Triangle Inequality Theorem |

Vertical Angles are congruent | Vertical Angles Congruence Theorem |

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

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

If two parallel lines are cut by a transversal, then the consecutive interior (co-interior) angles are supplementary | Consecutive Interior (Co-Interior) Angles Supplementary |

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

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

If two lines are cut by a transversal and co-interior angles are supplementary, then the two lines are parallel | Co-Interior Angles Converse |

If two lines are parallel to the same line, then they are parallel to each other | Transitive for Parallel Lines |

The sum of the measures of the interior angles of a triangle is 180 degrees | Triangle Sum Theorem |

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles | Exterior Angle Theorem |

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs | Pythagorean Theorem |

If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle | Converse of Pythagorean Theorem |

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent | Angle-Angle-Side (AAS) Congruence Theorem |

If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent | Angle-Side-Angle (ASA) Congruence Theorem |

If two sides of a triangle are congruent, then the angles opposite the sides are congruent | Base Angles Theorem |

If a triangle is equilateral, then the triangle is equiangular | Corollary to the Base Angles Theorem |

If two angles of a triangle are congruent, then the sides opposite the angles are congruent | Base Angles Converse |

If a triangle is equiangular, then the triangle is equilateral | Corollary to the Base Angles Converse |

If the corresponding side lengths of two triangles are proportional, then the triangles are similar | Side-Side-Side Similarity (SSS Sim) |

If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar | Side-Angle-Side Similarity (SAS Sim) |

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent | Hypotenuse-Leg (HL) Congruence |

If the square of the length of the longest side of a triangle is greater than the of the squares of the lengths of the other two sides, then the triangle is obtuse. | Pythagorean Obtuse Triangle Theorem |

If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths | Perimeters of Similar Polygons Theorem |

The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side | Midsegment Theorem |

If a point is on a perpendicular bisector of a segment, then it is on the perpendicular bisector of the segment | Perpendicular Bisector Theorem |

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment | Converse of the Perpendicular Bisector Theorem |

The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle | Circumcenter Theorem |

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle | Angle Bisector Theorem |

If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle | Converse of the Angle Bisector Theorem |

The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle | Incenter Theorem |

The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side | Cenroid Theorem |

If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original and to each other | Similar Right Triangles Theorem |

Created by:
warnockj