Right Triangles in Geometry Flashcards

Question 1

What is a right triangle?

Accepted Answer

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

Question 2

In a $45^\circ$-$45^\circ$-$90^\circ$ triangle, if a leg is $7$, what is the hypotenuse?

Accepted Answer

Hypotenuse $=7\sqrt{2}$.

Question 3

A right triangle has altitude to the hypotenuse splitting the hypotenuse into segments $p$ and $q$. Write the geometric-mean relationships.

Accepted Answer

Let hypotenuse be $c=p+q$, altitude be $h$, and legs be $a,b$. Then
$$h^2=pq,\quad a^2=cp,\quad b^2=cq.$$

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