The Triangle and its Properties

The point of concurrence of the medians is called the centroid. Which of the following is always true for the centroid?

In $\Delta PQR$, if $PS$ is the altitude to $QR$, then the measure of $\angle PSQ$ is:

If $AM$ is a median of $\Delta ABC$, the point $M$ must lie on:

In $\triangle ABC$, $\angle A = 32^\circ$ and $\angle B = 48^\circ$. Find the exterior angle at vertex $C$.

If an exterior angle is $138^\circ$ and one interior opposite angle is $68^\circ$, find the other.

An exterior angle is $115^\circ$. One of the interior opposite angles is $55^\circ$. Find the other.

The angles of a triangle are in the ratio $1:3:5$. Find the measure of the smallest angle.

If the sum of two angles $\angle A$ and $\angle B$ of a triangle is $100^\circ$, what is the measure of $\angle C$?

The angles of a triangle are $x-10, x,$ and $x+10$ degrees. Find the value of $x$.

If $XY = 7$, $YZ = 8$, and $ZX = 9$, which check confirms it is a triangle?

Can segments of $13\text{ cm}, 14\text{ cm},$ and $28\text{ cm}$ form a triangle?

If $a, b, c$ are sides of a triangle, then $b + c - a$ is always:

If the legs of a right triangle are $a$ and $b$, and the hypotenuse is $c$, then the area is given by:

If the base of a right triangle is $24 \text{ units}$ and the hypotenuse is $25 \text{ units}$, what is the perpendicular?

The set of three positive integers that satisfy the Pythagoras property is known as a: