Understanding Triangle Properties: Medians, Altitudes, and Centers Quiz

1) What are medians in a triangle?

Segments that connect the midpoints of two sides of a triangle

Segments that contain endpoints at the vertex of a triangle and at the midpoint of an opposite side

Perpendicular bisectors of the sides of a triangle

Lines connecting any two vertices in a triangle

Medians in a triangle are specific segments that connect a vertex with the midpoint of the opposite side, different from simply connecting any two vertices, connecting midpoints of sides, or being perpendicular bisectors of the sides.

Explanation

Medians in a triangle are specific segments that connect a vertex with the midpoint of the opposite side, different from simply connecting any two vertices, connecting midpoints of sides, or being perpendicular bisectors of the sides.

2) What are altitudes?

Segments that contain endpoints at the vertex of a triangle and at the perpendicular of an opposite side

Angles that measure less than 90 degrees in a triangle

Segments that divide a triangle into two congruent triangles

Lines connecting the midpoints of two sides of a triangle

Altitudes are segments that start at the vertex of a triangle and extend perpendicular to the opposite side. They are different from the other options provided, which describe midsegments, acute angles, and medians in a triangle.

Explanation

Altitudes are segments that start at the vertex of a triangle and extend perpendicular to the opposite side. They are different from the other options provided, which describe midsegments, acute angles, and medians in a triangle.

3) What is the centroid in a triangle?

The point where all the perpendicular bisectors meet in a triangle

The point where all the altitudes meet in a triangle

The point where all the angle bisectors meet in a triangle

The centroid is the point of concurrency of all the median(s) in a triangle, not to be confused with other points of concurrency such as altitudes, angle bisectors, or perpendicular bisectors.

Explanation

The centroid is the point of concurrency of all the median(s) in a triangle, not to be confused with other points of concurrency such as altitudes, angle bisectors, or perpendicular bisectors.

4) What is the Orthocenter?

The point where all angles of a triangle bisect

The point of concurrency of all the Altitude(s)

The center of a circle

The intersection of the medians

The Orthocenter is the point where all three altitudes of a triangle intersect, not to be confused with the center of a circle, the intersection of the medians, or the point where all angles bisect.

Explanation

The Orthocenter is the point where all three altitudes of a triangle intersect, not to be confused with the center of a circle, the intersection of the medians, or the point where all angles bisect.

5) What is an angle bisector?

A line segment that connects two non-consecutive vertices of a polygon

A line that divides an angle into two congruent angles

Segments that contain endpoints at the bisector of a triangle vertex and at an opposite side

A segment that connects the midpoints of two sides of a triangle

An angle bisector is a line or segment that divides an angle into two equal angles, not necessarily dividing the angle or creating congruent angles. The other incorrect options do not accurately describe what an angle bisector is.

Explanation

An angle bisector is a line or segment that divides an angle into two equal angles, not necessarily dividing the angle or creating congruent angles. The other incorrect options do not accurately describe what an angle bisector is.

6) What is the incenter?

The midpoint of a triangle

The point where all sides meet in a triangle

The intersection point of altitudes in a triangle

The incenter is defined as the center of the inscribed circle in a triangle, not to be confused with other points of concurrency or geometric centers.

Explanation

The incenter is defined as the center of the inscribed circle in a triangle, not to be confused with other points of concurrency or geometric centers.

7) What are perpendicular bisectors?

Segments that divide a figure into two congruent parts.

Segments that connect any two points on a circle.

Lines that intersect at a 90-degree angle.

Segments that contain endpoints at any position and is at the perpendicular midpoint of an opposite side

Perpendicular bisectors are lines or segments that meet at right angles and divide a given line segment into two equal parts. They are not necessarily related to dividing figures or connecting points on a circle.

Explanation

Perpendicular bisectors are lines or segments that meet at right angles and divide a given line segment into two equal parts. They are not necessarily related to dividing figures or connecting points on a circle.

8) What is a midsegment?

A segment that connects a vertex of a triangle with the midpoint of the opposite side

A line segment that connects any two points on a circle

A line connecting two non-adjacent vertices of a polygon

Segment that contains endpoints at the midpoint of one side and at the midpoint of another side

A midsegment is specifically defined as a segment that connects the midpoints of two sides of a triangle, not just any segment connecting points or vertices.

Explanation

A midsegment is specifically defined as a segment that connects the midpoints of two sides of a triangle, not just any segment connecting points or vertices.