Across
- 1. Every regular polygon and all triangles can be described as this, that is there is a circle that contains all of the shape's vertices.
- 5. This theorem states that three cevians, AY, BZ, and CX, of triangle ABC (where X,Y, and Z are points on the triangle's sides) are concurrent iff AX/XB * BY/YC * CZ/ZA = 1.
- 7. If angle 1 and angle 2 have a sum of 90 degrees, then angle 1 is a _____ of angle 2 and vice versa.
- 8. b is the geometric mean between a and c if a/b = b/c
- 9. In a triangle, this is the point in which the lines containing its altitudes are concurrent.
- 10. According to this theorem, if given, A-B-C, then, AB + BC = AC.
- 12. The angles in a linear pair are _____, that is, their sum is 180 degrees.
- 16. In a plane, two points equidistant from a line segment's endpoint determine the _____ _____ of that line segment.
- 18. According to this theorem, if a line parallel to one side of a triangle intersects the other two sides, it divides the sides in the same ratio. According to the corollary of this theorem, we can also know that in the figure, AD/AB = AE/AC and DB/AB = EC/AC
- 19. These are used to visualize how conditional statements relate to each other.
- 20. A figure has this with respect to a point iff it coincides with its rotation image through less than 360 degrees about the point.
- 23. Two angles form a _____ _____ iff they have a common side and their sides are opposite rays
- 24. If two angles of one triangle are equal to two angles of another triangle, you can't prove congruence but you can prove this.
- 26. The _____ of a parallelogram bisect each other.
- 28. If the angles in a linear pair are equal, then their sides are _____.
- 31. Euclid described this as, "that which has no part."
- 32. The _____ area of a sphere is 4 pi * the square of its radius
- 33. To find the area of a parallelogram one would find the product of any base and its corresponding one of these.
- 34. In a regular polygon, this is a perpendicular line segment from its center to one of its sides.
Down
- 2. By interchanging the hypothesis and conclusion of a conditional statement (changing a-->b to b-->a), you form its _____.
- 3. It is important to remember that when using the ASA or SAS postulates, you must use the _____ side for ASA and angle for SAS.
- 4. the angle bisectors of a triangle can be described as this.
- 6. A figure has this type of rotation symmetry if the smallest angle through which it can be turned to look exactly the same is 360 degrees/6.
- 7. This theorem states that if two angles are supplementary to the same third angle, them they are equal.
- 11. This is the point in a pyramid where the lateral edges meet.
- 13. You can describe lines as _____ if you have equal alternate interior angles, supplementary interior angles on the same side of a transversal, two lines perpendicular to a third line (in a plane), or equal corresponding angles.
- 14. In a circle, this is the region bounded by an arc of the circle and two radii, extending to the endpoints of that arc.
- 15. Two angles are _____ _____ iff the sides of one angle are opposite rays to the sides of the other.
- 17. This transformation maintains the distance and angle measures.
- 21. Three of these type of points determine a plane.
- 22. Vertical angles are always _____ to each other.
- 25. This is parallel to the third side of a triangle and half as long as it too.
- 27. In a triangle, the point in which the medians are concurrent
- 29. You can prove that two triangles are _____ if two angles and one of their opposite sides are equal to the corresponding parts of another triangle.
- 30. A/An _____ angle of a triangle is equal to the sum of the remote interior angles.