Chapter 5 Review

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

What are the possible side lengths of a triangle?

Back

The side lengths of a triangle must satisfy the Triangle Inequality Theorem.

Front

What is a centroid in a triangle?

Back

The centroid is the point where the three medians of a triangle intersect, and it is also the center of mass of the triangle.

Front

How do you find the range of values for a side of a triangle?

Back

To find the range of values for a side of a triangle, use the Triangle Inequality Theorem to set up inequalities based on the lengths of the other two sides.

Front

If two sides of a triangle are 16 and 19, what could be the length of the third side?

Back

The length of the third side must be greater than |16 - 19| and less than 16 + 19, so it must be between 3 and 35.

Front

What is the formula to find the centroid of a triangle with vertices (x1, y1), (x2, y2), (x3, y3)?

Back

The centroid (G) can be found using the formula: G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

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, and it is the center of the circumcircle.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is the center of the incircle.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the altitudes of a triangle intersect.

Front

How do you solve for x in a triangle given the lengths of segments?

Back

Set up an equation based on the relationships between the segments and solve for x.