Pythagorean Theorem flashcards for right triangles

Question 1

What is a right triangle?

Accepted Answer

A triangle with one angle equal to $90^\circ$. The side opposite the right angle is the hypotenuse.

Question 2

Evaluate $c$ for a right triangle with legs $6$ and $8$.

Accepted Answer

$c=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10$.

Question 3

State the converse of the Pythagorean Theorem and its distance-formula connection.

Accepted Answer

Converse: If a triangle with sides $a,b,c$ (with $c$ largest) satisfies $a^2+b^2=c^2$, then the triangle is right.
Connection: The distance formula $$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$ comes from the Pythagorean Theorem using horizontal and vertical leg lengths.

Pythagorean Theorem flashcards for right triangles

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