# Geometry

## Interior and Exterior Angles of Triangles

Directions: In triangle ABC, angle ABC is obtuse. Using the digits 1 to 9 at most one time each, place a digit in each box to make angle ACB the smallest possible acute angle. Source: Jay Sydow

## Maximum Volume of a Cylinder

Directions: Using the digits 0 to 9 at most one time each, place a digit in each box to give this cylinder the maximum volume possible. Source: Kyle Leinweber

## Triangle Sum Theorem

Directions: Using the digits 1-9 at most one time each, fill in the blanks so that when you solve for x, it is a whole number. Source: Franco D. Adkins

## Parallel and Perpendicular Lines

Directions: Using the digits 0 to 9, at most once each time, fill in blanks to create a set of 4 points that create either parallel or perpendicular lines, depending on how you connect them. ( ___, ___ ) ( ___, ___ ) ( ___, ___ ) ( ___, ___ ) Source: Bryan Anderson

## Interior Angles

Directions: Using the digits 0 through 9 at most one time, fill in the boxes to make the sum of the interior angles of a triangle. Source: Ashley Henderson

## Pythagorean Theorem 2

Directions: Using the digits 0 to 9, at most one time each, fill in the boxes to find the lengths of the missing sides such that the missing leg’s length is as long as possible. Source: Robert Kaplinsky

## Pythagorean Theorem

Directions: Using the digits 0 to 9, at most one time each, fill in the boxes to find two pairs of possible lengths for the missing sides. Source: Robert Kaplinsky

## Partitioning a Line Segment

Directions: Using the digits 1 to 8 exactly one time each, fill in the boxes to create a line segment AB, where between point A and point B, there exists a point P so that it partitions line segment AB into a ratio. Source: Jon Henderson

## 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

## Perimeter and Pythagorean Theorem

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