Example Problems: Is This a Right Triangle? Converse Method

📚 Quick Study Guide

• 📐 Pythagorean Theorem: For a right triangle with sides $a$, $b$, and hypotenuse $c$, the theorem states: $a^2 + b^2 = c^2$.
• 🔄 Converse of the Pythagorean Theorem: If for a triangle with sides $a$, $b$, and $c$, $a^2 + b^2 = c^2$, then the triangle is a right triangle.
• 🔍 Identifying the Hypotenuse: The hypotenuse is the longest side of the triangle and is opposite the right angle.
• 🧮 Steps:
  1. Identify the longest side (potential hypotenuse).
  2. Square all three sides.
  3. Check if the sum of the squares of the two shorter sides equals the square of the longest side.

Practice Quiz

1. Question 1: A triangle has sides of length 3, 4, and 5. Is it a right triangle?
   1. Yes
   2. No
   3. Cannot be determined
   4. Only if it's isosceles
2. Question 2: A triangle has sides of length 5, 12, and 13. Is it a right triangle?
   1. Yes
   2. No
   3. Only if the angle opposite the side of length 13 is 90 degrees
   4. It could be acute
3. Question 3: A triangle has sides of length 7, 8, and 11. Is it a right triangle?
   1. Yes
   2. No
   3. Only if one angle is obtuse
   4. It's always a right triangle
4. Question 4: A triangle has sides of length 6, 8, and 10. Is it a right triangle?
   1. Yes
   2. No
   3. Maybe
   4. Only if it's scalene
5. Question 5: A triangle has sides of length 9, 12, and 15. Is it a right triangle?
   1. Yes
   2. No
   3. Only if it's acute
   4. It's always a right triangle
6. Question 6: A triangle has sides of length 8, 15, and 17. Is it a right triangle?
   1. Yes
   2. No
   3. Only if the sides are integers
   4. Cannot be determined
7. Question 7: A triangle has sides of length 10, 24, and 26. Is it a right triangle?
   1. Yes
   2. No
   3. Only if the sides are rational
   4. It's an obtuse triangle