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Comprehensive Geometric Theorems For Integrated Math 2

Aahana C Math 9th grade Englisch 42 Karten

Comprehensive Geometric Theorems For Integrated Math 2

Karten in diesem Stapel (42)

  1. 1Segment Addition PostulateTwo Lengths of a Segment add up to become a full length
  2. 2Transitive Property of EqualityIf a=b and b=c then a=c
  3. 3Subtraction Property of EqualitySubtract expressions which are equal
  4. 4Angle Addition PostulateAdd two angle measures to make one large angle measure
  5. 5Substitution Property of EqualityIf x=y, then x can be substituted in for y and vice versa
  6. 6Pependicular Bisector TheoremIf a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segmentPependicular Bisector Theorem
  7. 7Converse of the Perpendicular Bisector TheoremIf a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segmentConverse of the Perpendicular Bisector Theorem
  8. 8Angle Bisector TheoremIf a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle.Angle Bisector Theorem
  9. 9Converse of the Angle Bisector TheoremIf a point is in the interior of an angle and is equidistant from the two sides of an angle, then it lies on the bisector of the angleConverse of the Angle Bisector Theorem
  10. 10Circumcenter TheoremThe circumcenter (a.k.a a point equidistant from the vertices of a triangle where three perpendicular bisectors of the sides meet) of a triangle is equidistant from the verticies of the triangleCircumcenter Theorem
  11. 11Incenter TheoremThe incenter (a.k.a a point equidistant from the sides of a triangle where three angle bisectors intersect) of a triangle is equidistant from the sides of the triangle.Incenter Theorem
  12. 12Centroid TheoremThe centroid (a.k.a a point two thirds the distance from each vertex to the midpoint of the opposite side) of a triangle is always two thirds the distance from a vertex to the midpoint of the opposite side.Centroid Theorem
  13. 13Triangle Midsegment TheoremThe segment connecting the midpoint of two sides of a triangle is parallel to the third side and is half as long to the third side.Triangle Midsegment Theorem
  14. 14Triangle Longer Side TheoremIf one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle facing the shorter sideTriangle Longer Side Theorem
  15. 15Triangle Larger Angle TheoremIf one angle of a triangle is larger than another angle, then the side opposite the larger angle will be longer than the side opposite the smaller angleTriangle Larger Angle Theorem
  16. 16Triangle Inequality TheoremThe sum of the lengths of any two sides of a triangle must always be larger than the third sideTriangle Inequality Theorem
  17. 17Hinge TheoremIf two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is larger than the third side of the secondHinge Theorem
  18. 18Converse of the Hinge TheoremConverse of the Hinge Theorem
  19. 19Base Angles TheoremIn an isoceles triangle, the angles opposite the congruent sides are congruentBase Angles Theorem
  20. 20Polygon Exterior Angles TheoremThe sum of the measures of the exterior angles of a convex polygon, at each vertex, is 360 degrees. To find each individual measure, divide 360 by n, n being the number of sidesPolygon Exterior Angles Theorem
  21. 21Parallelogram Opposite Sides TheoremIf a quadrilateral is a parallelogram, then the opposite sides are congruentParallelogram Opposite Sides Theorem
  22. 22Parallelogram Opposite Angles TheoremIf a quadrilateral is a parallelogram, then opposite angles are congruentParallelogram Opposite Angles Theorem
  23. 23Parallelogram Consecutive Angles TheoremIf a quadrilateral is a parallelogram, then the consecutive angles are supplementaryParallelogram Consecutive Angles Theorem
  24. 24Parallelogram Diagonal TheoremIf a quadrilateral is a parallelogram, then its diagonals bisect each otherParallelogram Diagonal Theorem
  25. 25Parallogram Opposite Sides Parallel and Congruent TheoremIf one pair of a quadrilateral's sides are congruent and parallel, then a quadrilateral is a parallelogramParallogram Opposite Sides Parallel and Congruent Theorem
  26. 26Parallelogram Diagonals ConverseIf the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram
  27. 27Rhombus CorollaryA quadrilateral is a rhombus if and only if it has four congruent sidesRhombus Corollary
  28. 28Rectangle CorollaryA quadrilateral is a rectangle if and only if it has four right anglesRectangle Corollary
  29. 29Square CorollaryA quadrilateral is a square if and only if it is a rhombus and a rectangleSquare Corollary
  30. 30Rhombus Diagonals TheoremA parallelogram is a rhombus if and only if its diagonals are perpendicular
  31. 31Triangle Sum TheoremThe sum of the three interior angles of a triangle adds up to 180 degreesTriangle Sum Theorem
  32. 32Exterior Angle TheoremThe measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles, and is equal to the sum of the other two interior anglesExterior Angle Theorem
  33. 33Polygon Interior Angles TheoremThe sum of the interior angles of a polygon is equal to (n-2)*180, where n is the number of sides. To find each individual measure, divide (n-2)*180/nPolygon Interior Angles Theorem
  34. 34Polygon Exterior Angles TheoremThe sum of the measure of the exterior angles of a convex polygon, one angle at each vertex, is 180Polygon Exterior Angles Theorem
  35. 35Corollary to the Polygon Interior Angles TheoremThe sum of the measures of the interior angles of a quadrilateral is 360 degrees, a triangle is 180, a pentagon 720, etc
  36. 36Parallelogram Opposite Sides TheoremIf a quadrilateral is a parallelogram, then opposite sides are congruentParallelogram Opposite Sides Theorem
  37. 37Parallelogram Opposite Angles TheoremIf a quadrilateral is a parallelogram, then opposite angles are congruentParallelogram Opposite Angles Theorem
  38. 38Parallelogram Consecutive Angles TheoremIf a quadrilateral is a parallelogram, then consecutive angles are supplementaryParallelogram Consecutive Angles Theorem
  39. 39Parallelogram Opposite Sides Parallel and Congruent TheoremIf one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogramParallelogram Opposite Sides Parallel and Congruent Theorem
  40. 40Rhombus CorollaryA quadrilateral is a rhombus if and only if it has four congruent sidesRhombus Corollary
  41. 41Parallelogram Diagonals The0remA quadrilateral is a parallelogram if its diagonals bisect each otherParallelogram Diagonals The0rem
  42. 42Rectangle CorollaryA

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Beschreibung
A set of flashcards detailing many geometric theorems including theorems on triangles, quadrilaterals, triangle similarity, circles, basic trignometry, etc.
Erstellt von
Aahana C
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