Across
- 3. If a triangle with side 5 is dilated by a scale factor of 2, the new corresponding side length is this.
- 4. If two triangles are mathematically similar, the difference between their corresponding angle measures is exactly this.
- 6. The parallel sides of a parallelogram cut by a diagonal create these interior angles, proving the inner triangles similar.
- 9. In a right triangle, if the legs are 3 and 4, the hypotenuse is this length, creating a base for similar dilations.
- 12. A mathematical comparison of two side lengths in a triangle.
- 13. A line that passes through two or more lines.
- 14. In any two similar equilateral triangles, every single interior angle measures exactly this many degrees.
- 15. When solving a proportion, the product of the extremes equals the product of these.
- 17. A segment connecting the midpoints of two sides of a triangle, creating a smaller similar triangle inside.
- 20. These segments bisect each other in a parallelogram, splitting it into similar compound triangles.
- 23. If two triangles are similar and one is a right triangle, the other must have an angle measuring exactly this.
- 24. If a shape has a side of 10 and its similar image has a corresponding side of 20, the scale factor is this.
- 28. When a parallelogram's diagonals bisect each other, the center intersection forms these congruent angles for similar triangles.
- 29. When solving a proportion, the product of these equals the product of the means.
- 32. The midsegment of a triangle is strictly _________ to the base of the triangle.
- 33. The theorem proving triangles are similar if all three pairs of sides are proportional.
- 35. A famous theorem used alongside similarity proportions to find missing sides of right triangles.
- 37. A midsegment creates a smaller nested triangle exactly ____ the size of the large one.
- 39. If the ratio of corresponding sides is 1 to 3 and the smaller side is 3, the larger corresponding side is this.
- 40. The geometric mean of 4 and 16, representing the altitude drawn to the hypotenuse of a right triangle.
- 41. If a similar triangle is dilated by a scale factor of 5, a side measuring 5 units becomes this many units long.
- 43. The longest side of a right triangle, which must be carefully matched when setting up similarity ratios.
- 46. Matching angles or sides between two similar triangles.
- 47. Figures like two triangles with the exact same shape but different sizes.
- 48. A parallelogram whose diagonals perpendicularly bisect each other, forming four similar right triangles.
Down
- 1. The specific type of angle positioned strictly between two given sides of a triangle.
- 2. A four-sided polygon whose bisecting diagonals create opposite pairs of similar triangles.
- 5. A term used when a polygon is divided into two equal parts by a line.
- 7. An equation setting the side ratios of two triangles equal to each other.
- 8. If a 3-4-5 right triangle is dilated by a factor of 4, the length of the new corresponding middle leg is this.
- 9. If the ratio of two corresponding sides is 1 to 4 and the smaller side is 10, the larger side is this.
- 10. If a side of 6 corresponds to a side of 12, then a side of 9 corresponds to a side of this length.
- 11. If a midsegment is 3.5 units long, the parallel base of the larger triangle is exactly this many units.
- 16. The theorem requiring two proportional sides and a congruent angle trapped between them.
- 18. The midsegment of a triangle is parallel to a base of 40; the midsegment's length is this.
- 19. If two similar triangles have corresponding angles, and one is 50 degrees, the matching angle is this many degrees.
- 21. A scale multiplier of exactly this amount means the two triangles are actually congruent, not just similar.
- 22. A perpendicular line segment drawn from a right triangle's highest point down to its base.
- 25. The number of small similar triangles formed when the diagonals of a rhombus bisect each other.
- 26. If a 2-foot stick casts a 4-foot shadow, a 3-foot stick casts a shadow of this many feet.
- 27. In similar triangles, these matching line segments are always proportional.
- 30. In similar triangles, if side A is 3 and side B is 4, a similar triangle with side A as 9 will have side B as this.
- 31. The postulate stating triangles are similar if just two pairs of angles are congruent.
- 33. The exact multiplier used to scale a smaller triangle up to a larger one.
- 34. In similar isosceles right triangles, the two acute angles always measure exactly this many degrees.
- 36. In similar triangles, these matching corners are always perfectly congruent.
- 38. Another term for the points of the angles.
- 42. The two shorter sides of a right triangle.
- 44. If a triangle's side is reduced from 30 down to 10, the scale factor is one _____.
- 45. If the corresponding sides of two similar triangles are in a 1 to 2 ratio, a side of 2 in the smaller triangle matches a side of this length.