| J.T.'s Geometry Site |
| Conjectures | Definitions | Figures and Polygons |
| Geometry Story | Biographies | Math Funnies |
|
1. If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints
2. If a point is equally distant from the endpoints of a segment then it is on the perpendicular bisector of the segment 3. The shortest distance from a point to a line is measured along the perpendicular from the point to the line 4. If a point is on the bisector of an angle, then it is equidistant from the sides of the angle 5. The measure of each angle of an equilateral triangle is 60 degrees 6. The three angle bisectors of a triangle are concurrent (they meet in a point) 7. The three perpendicular bisectors of a triangle are concurrent 8. The three altitudes of a triangle are concurrent 9. The circumcenter of a triangle is equidistant from all the vertices of a triangle 10. The incenter of a triangle is equidistant to all three sides of the triangle 11. The three medians of a triangle are concurrent 12. The centroid of a triangle divides each median into two parts so that the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint 13. The centroid, cicumcenter, and orthocenter are the three points of concurrency on the Euler line. 14. If two angles are vertical angles, they are congruent 15. If two angles are a linear pair of angles, then they add up to 180 degrees. 16. If two parallel lines are cut by a transversal, then corresponding angles are congruent, alternate interior angles are congruent, and alternate exterior angles are congruent. 17. If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent alternate interior angles, and congruent alternate exterior angles, then the lines are parallel. 18. If (X1, Y1) and (X2, Y2) are the coordinates of the endpoints of a segment, then the coordinates of the midpoint are ( {X1 plus X2} / 2 , {Y1 plus Y2} /2 ) 19. In a coordinate plane, two distinct lines are parallel if and only if their slopes are the same 20. In a coordinate plane, two non-vertical lines are perpendicular if and only if their slopes are the negative reciprocal of each other. 21. If the coordinates of points A and B are (X1, Y1) and (X2, Y2) respectively, then AB squared = A squared plus B squared and AB is the square root of A squared plus B squared. 22. The three interior angles of a triangle add up to 180 degrees 23. If two angles of one triangle are equal in measure to two angles of another triangle, then the third angle in each triangle is congruent 24. If a triangle is isosceles, then the measure of the base angles will be equal 25. If a triangle has congruent base angles, then it has two congruent sides 26. An equilateral triangle is equiangular, and conversely, an equiangular triangle is equilateral 27. The sum of the lengths of any two sides of a triangle is greater than the length of the third side 28. In a triangle, the greatest angle is opposite the greatest side, the second largest angle is opposite the second largest side, and the smallest angle is opposite the smallest side 29. The measure of an exterior angle of a triangle is equal to the sum of the remote interior angles 30. If the three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent 31. If two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the two triangles are congruent. 32. If two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the two triangles are congruent. 33. If two angles and a side that isn�t between them in one triangle is congruent to two angles and a side that isn�t between them in another triangle, then the triangles are congruent. 34. In an isosceles triangle, the bisector of the vertex angle is also the altitude to the base and the median to the base. 35. The sum of n interior angles of an n-gon is (n-2)180 degrees 36. The sum of one set of exterior angles is 360 degrees 37. The measure of each angle of a regular n-gon can be found by: (n-2)180 divided by n 38. The diagonals of a kite are perpendicular 39. The diagonal connecting the vertex angles of a kite is the bisector of the other diagonal 40. The non-vertex angles of a kite are congruent 41. The vertex angles of a kite are bisected by a diagonal 42. The consecutive angles between the bases of a trapezoid are supplementary angles 43. The base angles of an isosceles trapezoid are congruent 44. The diagonals of an isosceles trapezoid are congruent 45. The 3 midsegments of a triangle divide the triangle into four congruent, smaller triangles. 46. A midsegment of a triangle is parallel to the third side and half the length of the base 47. The midsegment of a trapezoid is parallel to the bases and is congruent in length to one half the sum of the two bases 48. The opposite angles of a parallelogram are congruent 49. The consecutive angles of a parallelogram are supplementary 50. The opposite sides of a parallelogram are congruent 51. The diagonals of a parallelogram are congruent 52. If two parallel lines are intersected by a second pair of parallel lines the same distance apart as the first pair, then the parallelogram formed is a rhombus 53. The diagonals of a rhombus are perpendicular bisectors of eachother 54. The diagonals of a rhombus bisect the angles of the rhombus 55. The measure of each angle of a rectangle is 90 degrees 56. The diagonals of a rectangle are congruent 57. If the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar 58. If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar 59. If two similar polygons (or circles) have lengths of corresponding sides (or radii) in the ratio of m/n, then their areas are in the ratio of m squared divided by n squared 60. If two similar shapes have corresponding dimensions in the ratios of m divided by n then their volumes are in the ratio of m cubed over n cubed 61. In a right triangle the altitude to hypotenuse forms two triangles, each similar to the original triangle, and each similar to each other 62. If two triangles are similar, then the corresponding altitudes, medians, and angle bisectors are proportional to the corresponding sides. 63. If two chords in a circle are congruent, then they determine two central angles that are congruent 64. If two chords in a circle are congruent, then their arcs are congruent 65. The perpendicular from the center of a circle to a chord is the bisector of the chord 66. Two congruent chords in a circle are equidistant from the center of the circle 67. The perpendicular bisector of a chord runs through the center of the circle 68. A tangent to a circle is perpendicular to the radius drawn to the point of tangency 69. Tangent segments to a circle from a point outside the circle are congruent 70. The measure of an inscribed angle in a circle is half the measure of the intercepted arc 71. Inscribed angles that intercept the same arc are congruent 72. Angles inscribed in a semicircle 90 degrees 73. The opposite angles of a quadrilateral inscribed in a circle are supplementary 74. Parallel lines intercept congruent arcs on a circle 75. If C is the circumference and D is the diameter of a circle, then there is a number pi such that C = pi(diameter) Because D = 2r where r is the radius, then C = 2r(pi) 76. The length of an arc equals the arc measure divided by 360, times the circumference |