Geometry Ch 15 Quiz

Line AD is an angle bisector in the triangle. An angle bisector is a line that divides an angle into two equal parts. In this case, line AD divides one of the angles in the triangle into two equal angles. This means that line AD cuts through the angle and splits it into two smaller angles of equal measure. Therefore, line AD is an angle bisector in the triangle.

Line AD is the median of the triangle. A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side. In this case, line AD connects vertex A to the midpoint of side BC. Medians are important in triangles as they intersect at a point called the centroid, which divides each median into two segments in a 2:1 ratio. The centroid is also the center of gravity of the triangle.

The orthocenter is the point where the altitudes of a triangle intersect. An altitude is a line segment drawn from a vertex of the triangle perpendicular to the opposite side. Therefore, the correct answer is altitudes.

A perpendicular bisector is a line, segment, or ray that intersects a given segment at its midpoint and forms a right angle with it. It divides the segment into two equal parts and is equidistant from the endpoints of the segment. This term is commonly used in geometry to describe a line that cuts another line into two equal halves at a right angle.

The Angle Bisector Theorem states that if a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. In other words, if a line divides an angle into two equal angles, any point on that line will be the same distance away from each of the two sides of the angle.

The red line to the triangle is an altitude. An altitude is a line segment that extends from a vertex of a triangle perpendicular to the opposite side. It can be used to find the height or distance from a vertex to the base of the triangle.

Concurrent lines refer to three or more lines that intersect at a common point. This point of intersection is known as the point of concurrency. Therefore, concurrent lines are the correct term for three or more lines that meet in one point.

The term for the point of concurrency of the medians is the centroid. The centroid is the point where all three medians of a triangle intersect. It is also known as the center of gravity of the triangle, as it is the balance point of the triangle's mass. The centroid divides each median into two segments, with the length of the segment from the vertex to the centroid being twice as long as the segment from the centroid to the midpoint of the opposite side.

The Perpendicular Bisector Theorem states that if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. In other words, the distance from the point to each endpoint of the segment is equal. This theorem is specifically applicable to perpendicular bisectors, which are lines that intersect the given segment at a right angle and divide it into two equal halves. It does not apply to ordinary bisectors or lines that are not perpendicular to the segment.

The term for the point of concurrency of the perpendicular bisectors of the sides of a triangle is the circumcenter. The circumcenter is the center of the circumcircle, which is a circle that passes through all three vertices of the triangle. It is the point equidistant from all three vertices, and the perpendicular bisectors of the sides intersect at this point.

The incenter is the point of concurrency of the angle bisectors of a triangle. The angle bisectors of a triangle are the lines that divide each angle into two equal parts. The incenter is the center of the inscribed circle in the triangle, which is the largest circle that can fit inside the triangle.

The line DE is the midsegment of the triangle. A midsegment is a line segment that connects the midpoints of two sides of a triangle. In this case, DE connects the midpoints of two sides of the triangle, making it the midsegment.

The Triangle Midsegment Theorem states that if a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half its length. In this case, the correct answer states that the segment joins the midpoints of two sides of a triangle, making it parallel to the third side, and its length is half the length of the third side.