Similarity, Right Triangles, and Trigonometry

Directions: Using the digits 0 to 9 at most one time each and as many leading zeros as you like, place a digit in each box to create two similar triangles. Source: Drew Ross

Directions: Using the digits 0 to 9 at most one time each, place a digit in each box to create a right triangle where 𝜃 is as close to 10° as possible. Source: Thomas Derstein

Directions: Using the digits 1 through 6 at most one time each, fill in the boxes to find three side lengths that are two-digits each and form an acute triangle. Source: Samantha Cruz

Directions: Use the integers 2 through 10, at most one time each, as lengths of individual sides to form three triangles. What is the smallest total area of the three triangles you can create? What is the largest? Source: Dan Wulf

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes 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 …

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

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