Printable 45-45-90 triangle practice problems with answer key

📚 Topic Summary

A 45-45-90 triangle is a special right triangle where two angles are each 45 degrees, and one angle is 90 degrees. Because the two angles are equal, the two legs opposite those angles are also equal. If we let the length of each leg be $x$, then the length of the hypotenuse is $x\sqrt{2}$. This relationship makes solving for missing sides much easier!

Understanding these relationships is key to quickly solving problems involving 45-45-90 triangles. The worksheet below provides practice to reinforce these concepts.

🧮 Part A: Vocabulary

Match the term with its definition:

1. Term: Leg
2. Term: Hypotenuse
3. Term: 45-45-90 Triangle
4. Term: Isosceles Triangle
5. Term: Right Triangle

1. Definition: A triangle with one 90-degree angle.
2. Definition: The side opposite the right angle in a right triangle.
3. Definition: A triangle with angles measuring 45, 45, and 90 degrees.
4. Definition: One of the two shorter sides in a right triangle.
5. Definition: A triangle with two equal sides and two equal angles.

✍️ Part B: Fill in the Blanks

A 45-45-90 triangle is a special type of ______ triangle. The two legs are ______, and the hypotenuse is always the length of a leg times ______. If one leg is 5, then the other leg is ______ and the hypotenuse is ______.

🤔 Part C: Critical Thinking

Explain how knowing the length of the hypotenuse of a 45-45-90 triangle allows you to find the length of each leg. Provide an example.

✅ Answer Key

Part A: Vocabulary

• 🔍 Leg - One of the two shorter sides in a right triangle.
• 📐 Hypotenuse - The side opposite the right angle in a right triangle.
• 📐 45-45-90 Triangle - A triangle with angles measuring 45, 45, and 90 degrees.
• 📐 Isosceles Triangle - A triangle with two equal sides and two equal angles.
• 📐 Right Triangle - A triangle with one 90-degree angle.

Part B: Fill in the Blanks

A 45-45-90 triangle is a special type of isosceles right triangle. The two legs are equal, and the hypotenuse is always the length of a leg times $\sqrt{2}$. If one leg is 5, then the other leg is 5 and the hypotenuse is $5\sqrt{2}$.

Part C: Critical Thinking

If you know the length of the hypotenuse, you can find the length of each leg by dividing the hypotenuse by $\sqrt{2}$. For example, if the hypotenuse is $10\sqrt{2}$, then each leg is $10\sqrt{2} / \sqrt{2} = 10$.