Geometry Chapter 5 Test

Without any additional information or measurements provided in the diagram, it is not possible to determine which angle has the greatest measure. Therefore, the correct answer is "cannot be determined".

In order for a set of numbers to represent the lengths of the sides of a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In the given set, the sum of the lengths of the two smaller sides (7 and 11) is equal to the length of the longest side (18), violating the triangle inequality theorem. Therefore, the set 7, 11, 18 cannot represent the lengths of the sides of a triangle.

The given answer states that DH is greater than GH. This implies that DH is larger or has a higher value than GH.

The centroid of a triangle is the point of concurrency of the medians. A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. The centroid is located two thirds of the distance from each vertex to the midpoint of the opposite side. Therefore, the correct answer is centroid.

The circumcenter is the point of concurrency of the perpendicular bisectors of a triangle. It is equidistant from the vertices of the triangle, meaning that the distance from the circumcenter to each vertex is the same. This property makes the circumcenter the center of the circumcircle, which is a circle that passes through all three vertices of the triangle.

The incenter of a triangle is the point of concurrency of the angle bisectors. It is the center of the inscribed circle, which is equidistant from all three sides of the triangle. Therefore, the given statement is true and the correct answer is "Incenter".

The given answer states that m∠RST is greater than m∠TRS. This implies that the measure of angle RST is larger than the measure of angle TRS.