Question
Match each statement to the correct option provided.
In a right-
angled
triangle, the
square of the
hypotenuse
side equals
the sum of
the squares
theose…
Euclidean Theorem
sides.
In a right-
angled
triangle, the
square of the
hypotenuse
side equals
the sum of
the squares
theose…
Euclidean Theorem
sides.
Ask by Evans Garrett. in the United States
Jan 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
- Pythagorean Theorem: In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other sides.
- The Converse of Pythagorean theorem: If the square of one side equals the sum of the squares of the other two sides, then the triangle is right-angled.
Solution
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The Deep Dive
The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Picture a right triangle where the sides measure 3 units and 4 units; you’ll find that the hypotenuse will measure 5 units, which is derived from the equation
Now, as for the Converse of the Pythagorean theorem, it goes the other way around! If you have a triangle where the square of one side equals the sum of the squares of the other two, then you’ve got yourself a right triangle. It’s like a secret handshake for triangles! If you pick any three lengths and they fit this condition, you can be sure to whip out the protractor and declare it a right angle. How fun is that?
