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# High School: Geometry

## Law of Cosines Triangle

Directions: Use the numbers 1-9 (using each number no more than once) to fill in the circles of a triangle. The sum of the numbers on each side of the triangle is equal to the length of that side. What is the triangle with the largest (or smallest) angle measure that you can make? Source: Erick Lee

## Maximizing Volume of a Cylinder, Given Lateral Area

Directions:  Find at least 3 possible measures for the height and the radius of a cylinder with a lateral area of 144pi square centimeters. Which of your dimensions will give you the largest volume? Source:  Jason Miller

## Create Squares

Directions: Create a square with one of the vertices at (2,3). Fill in the blanks with whole numbers 0 through 9, using each number at most once, to show the rest of the vertices of the square. Bonus: Find more than one set of vertices. Source: John Mahlstedt

## Finding the Length of a Right Triangle’s Altitude

Directions: The black triangle is a right triangle with legs 8 and 6. The vertices are at the points (0,0), (0,8), and (6,0). The red line segment is perpendicular to hypotenuse. Find the length of the red line segment. Source: Kate Nerdypoo

## Parallel Lines and Perpendicular Transversals

Directions: Using the whole numbers 1 through 9 no more than one time each, fill in the boxes so that 2 of the lines are parallel and the third line is a transversal that is as close to perpendicular to the parallel lines as possible. Source: Shelli Foust and Robert Kaplinsky

## Parallel Lines and Transversals

Directions: Using the whole numbers 1 through 9 no more than one time each, fill in the boxes so that 2 of the lines are parallel and the third line is a transversal. Source: Shelli Foust

## Perpendicular Lines and Slope

Directions: Fill in the boxes with the digits 1 through 9 so that the lines through each pair of points are perpendicular. Use each digit at most once. Source: Nanette Johnson

## Parallel Lines and Slope

Directions: Fill in the boxes with the digits 1 through 9 so that the lines through each pair of points are parallel. Use each digit at most once. Source: Nanette Johnson