Geometry

Directions: What could the lengths of the legs be such that the lengths are integers and x is an irrational number between 5 and 7? Source: Daniel Luevanos

Directions: What is the fewest number of transformations needed to take pre-image ABCD to image A’B’C’D’? Source: Robert Kaplinsky

Directions: List three sequences of transformations that take pre-image ABCD to image A’B’C’D’. Source: Robert Kaplinsky

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to create two points that are equidistant from (4,-1). Source: Bryan Anderson

Directions: What is the side length of an equilateral triangle that has an area of 5 square units? Source: Robert Kaplinsky

Directions: Find the length of side x in the diagram below Source: Dylan Kane

Directions: How many points with two integer coordinates are 5 units away from (-2, 3)? Source: Dylan Kane

Directions: A cone is twice as tall as a cylinder of the same radius. What is the ratio of their volumes? Source: Dylan Kane

Directions: If n is equal to the number of sides, when is the sum of the interior angles less than (or greater than or equal to) the sum of the exterior angles? Source: Ricardo Navarro, Gladys Velasquez, Bryan Aguilar, and Eddie Galaviz

Directions: If n is equal to the number of sides on a regular polygon, what is the lowest value of n where each interior angle’s measure is less (or greater) than the exterior angle? Source: Ricardo Navarro, Gladys Velasquez, Bryan Aguilar, and Eddie Galaviz