Practice Math Questions for Praxis: Pythagorean Theorem

If you encounter a right triangle question on the Praxis Core exam, you can use good old Pythagoras' theorem to work out the answer. In some cases, you'll be able to skip the calculations and solve the problem using the properties of common right triangles!

Both of the following practice questions can be worked out using the Pythagorean theorem—but if you know your common right triangles, you'll be done before you can say "Eureka!"

Practice questions

1. For right triangle ABC, what is the measure of side AB?

   

   A. 64 m B. 36 m C. 18 m D. 4 m E. 8 m

2. A triangle has sides of 24 dm, 10 dm, and 26 dm. Is the triangle a right triangle?

   A. Yes B. No

Answers and explanations

1. The correct answer is Choice (E). For every right triangle, the square of the hypotenuse is equal to the sum of the squares of its legs. The legs are the sides that form the right angle, and the hypotenuse is the side that's across from the right angle. The formula is commonly represented as a² + b² = c², where a and b are the legs and c is the hypotenuse. Fill in what is known and solve for what is unknown:

   

   AB is 8 m.

   Knowing the side lengths of common right triangles can shave off much-needed time. For example, well-known right triangles include the 3-4-5 triangle (and its multiples, such as the 6-8-10 and the 9-12-15), the 5-12-13 triangle, and the 8-15-17 triangle. Based on this information, you could have known the other side length would be 8 without using the Pythagorean theorem.

2. The correct answer is Choice (A).
   If the triangle is a right triangle, the Pythagorean theorem applies to it — that is, the sum of the squares of the two leg measures equals the square of the hypotenuse. You can substitute the triangle's measures into a² + b² = c² and see whether the equation works:

   

   The equation is true, so the triangle is a right triangle.