Chapter 9, Problem 17CUR

(a)

To determine

To find: Position of points of intersection of medians in a right triangle.

Answer to Problem 17CUR

inside

Explanation of Solution

A triangle in which one angle is equal to $90°$ is known as a right-angled triangle.

In a triangle, a median is a segment joining vertex of the triangle to the midpoint of the opposite side.

In a right-angled triangle, the medians intersect inside the triangle

(b)

To determine

To find: Position of points of intersection of altitudes in a right triangle.

Answer to Problem 17CUR

on

Explanation of Solution

A triangle in which one angle is equal to $90°$ is known as a right-angled triangle.

In a triangle, an altitude is a segment from the vertex of the triangle perpendicular to the opposite side.

In a right-angled triangle, the altitudes intersect on the triangle

(c)

To determine

To find: Position of points of intersection of perpendicular bisectors in a right triangle.

Answer to Problem 17CUR

on

Explanation of Solution

A triangle in which one angle is equal to $90°$ is known as a right-angled triangle.

In a triangle, a segment from the vertex of the triangle that is both perpendicular to the opposite side and also bisects the opposite side is a perpendicular bisector.

In a right-angled triangle, the perpendicular bisectors intersect on the triangle.