Question

1. choose the correct answer.

you are dealing with a(n)____if a perpendicular segment intersects the side of a triangle at the midpoint.

incenter

centroid

circumcenter

orthocenter

1. choose the correct answer.

according to the centroid theorem, the____of a triangle is located 2/3 of the distance between the vertex and the midpoint of the opposite side of the triangle along each median.

midpoints

circumcenter

orthocenter

centroid

Explanation:

• For 7):
• The in - center is the point of intersection of the angle bisectors of a triangle.
• The centroid is the point of intersection of the medians of a triangle.
• The circum - center is the point of intersection of the perpendicular bisectors of the sides of a triangle. A perpendicular bisector is a perpendicular segment that intersects a side of a triangle at its mid - point.
• The ortho - center is the point of intersection of the altitudes of a triangle.
• For 8):
• Mid - points are just the middle points of the sides of a triangle.
• The circum - center is related to the perpendicular bisectors.
• The ortho - center is related to the altitudes.
• The centroid theorem states that the centroid of a triangle is located \(\frac{2}{3}\) of the distance between the vertex and the mid - point of the opposite side along each median.

Answer:

1. circumcenter
2. centroid