10.1-10.3 Review

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is equidistant from all three vertices of the triangle.

Front

How do you find the length of a segment in a triangle given the circumcenter?

Back

To find the length of a segment from the circumcenter to a vertex, use the property that all segments from the circumcenter to the vertices are equal in length.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.

Front

How do you calculate the measure of an angle in a triangle given the incenter?

Back

Use the properties of angles in a triangle and the fact that the sum of angles in a triangle is 180° to find the unknown angle.

Front

What is the relationship between the angles formed by the incenter and the triangle's vertices?

Back

The angles formed by the incenter and the triangle's vertices are related through the angle bisector theorem, which states that the incenter divides the angles into two equal parts.

Front

If m∠BCG = 29° and m∠CEA = 90°, how do you find m∠EAC?

Back

Use the fact that the sum of angles in triangle ACE is 180°. Therefore, m∠EAC = 180° - (m∠BCG + m∠CEA).

Front

What is the formula for the sum of angles in a triangle?

Back

The sum of the interior angles of a triangle is always 180°.

Front

How do you solve for x in an equation?

Back

To solve for x, isolate x on one side of the equation using inverse operations.

Front

What is the significance of the circumradius in a triangle?

Back

The circumradius is the radius of the circumcircle, which is the circle that passes through all three vertices of the triangle.

Front

What is the significance of the inradius in a triangle?

Back

The inradius is the radius of the incircle, which is the circle that is tangent to all three sides of the triangle.