Chp 5 Vocabulary

1. What does the term 'equidistant' mean?

Being far away from a point.

Moving at a variable distance from a point.

The same distance away from a point.

Having no distance at all.

The term 'equidistant' refers to objects or points that are at the same distance from a specific point or line. It does not refer to having no distance, being far away, or having a variable distance.

Explanation

The term 'equidistant' refers to objects or points that are at the same distance from a specific point or line. It does not refer to having no distance, being far away, or having a variable distance.

2. What are medians in a triangle?

Segments connecting the midpoints of two sides of a triangle.

Segments that bisect the angles of a triangle.

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

Segments connecting two adjacent vertices of a triangle.

The correct definition of medians in a triangle involves segments connecting the vertex to the midpoint of the opposite side, not adjacent vertices, midpoints of sides, or angle bisectors.

Explanation

The correct definition of medians in a triangle involves segments connecting the vertex to the midpoint of the opposite side, not adjacent vertices, midpoints of sides, or angle bisectors.

3. What is a centroid in geometry?

The point of concurrency of all the medians. The segment attached to the vertex is 2/3 of the length of the whole line.

The point of concurrency of all the altitudes. The segment attached to the vertex is half of the length of the whole line.

The point where all three angle bisectors intersect. The segment attached the vertex is 3/4 of the length of the whole line.

The midpoint of the triangle. It is equidistant from all three vertices.

In geometry, a centroid is the point where all three medians of a triangle intersect. A median is a line segment drawn from a vertex to the midpoint of the opposite side. The centroid divides each median into two segments, with the segment attached to the vertex being 2/3 of the length of the whole line. It is not the same as the point of concurrency of altitudes or angle bisectors.

Explanation

In geometry, a centroid is the point where all three medians of a triangle intersect. A median is a line segment drawn from a vertex to the midpoint of the opposite side. The centroid divides each median into two segments, with the segment attached to the vertex being 2/3 of the length of the whole line. It is not the same as the point of concurrency of altitudes or angle bisectors.

4. What are altitudes in relation to a triangle?

None of the above answers are correct.

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

The longest side of a triangle.

Segments that connect the midpoints of two sides of a triangle.

Lines that connect the midpoints of two sides of a triangle.

Altitudes in a triangle are segments that start at a vertex and are perpendicular to the opposite side. The incorrect answers provided do not accurately define altitudes.

Explanation

Altitudes in a triangle are segments that start at a vertex and are perpendicular to the opposite side. The incorrect answers provided do not accurately define altitudes.

5. What is the orthocenter of a triangle?

The intersection point of all the bisectors of a triangle.

The point where the perpendicular bisectors of a triangle's sides meet.

The point of concurrency of all the altitudes of a triangle.

A point where all the medians of a triangle intersect.

The orthocenter of a triangle is the point where all the altitudes (perpendicular lines from the vertices to the opposite sides) intersect.

Explanation

The orthocenter of a triangle is the point where all the altitudes (perpendicular lines from the vertices to the opposite sides) intersect.

6. What are angle bisectors?

Angles that are exactly 90 degrees.

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

Points where two sides of a triangle intersect.

Lines that go through the center of a triangle.

Angle bisectors are segments that divide an angle into two equal angles. They connect the vertex of a triangle with the opposite side, bisecting the angle.

Explanation

Angle bisectors are segments that divide an angle into two equal angles. They connect the vertex of a triangle with the opposite side, bisecting the angle.

7. What is the incenter of a triangle?

The point of concurrency of all the Angle Bisectors and is equidistant from all sides.

The incenter is the point where all three altitudes intersect.

The incenter is the point where all three medians intersect.

The incenter is the point where all three perpendicular bisectors intersect.

The incenter is the point where all the angle bisectors of a triangle intersect and is equidistant from all sides. It is not to be confused with other points of concurrency like the orthocenter, centroid, or circumcenter.

Explanation

The incenter is the point where all the angle bisectors of a triangle intersect and is equidistant from all sides. It is not to be confused with other points of concurrency like the orthocenter, centroid, or circumcenter.

8. What are Perpendicular Bisectors?

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

Segments that are equal in length and perpendicular to each other.

Lines that are equidistant from each other and never intersect.

Parallel lines that intersect at a right angle.

Perpendicular bisectors are segments that intersect at right angles and divide a line segment into two equal parts, with one endpoint at any position and the other at the perpendicular midpoint of the opposite side.

Explanation

Perpendicular bisectors are segments that intersect at right angles and divide a line segment into two equal parts, with one endpoint at any position and the other at the perpendicular midpoint of the opposite side.

9. What is the Circumcenter of a triangle?

The center of gravity of a triangle

The midpoint of a triangle

The point where all medians intersect

The point of concurrency of all Perpendicular Bisectors and is equidistant to all sides.

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect, making it equidistant from all three sides.

Explanation

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect, making it equidistant from all three sides.

10. What is the definition of a midsegment in geometry?

Segments that bisect each other at the middle of the sides.

Segments that connect the midpoint of one side to the midpoint of another side.

Segments that are perpendicular to each other at the midpoint of the sides.

Segments that contain endpoints at the midpoint of one side and the the midpoint of the other side.

A midsegment in geometry refers to a segment that connects the midpoints of two sides of a triangle. It does not necessarily have to be perpendicular or bisect the sides.

Explanation

A midsegment in geometry refers to a segment that connects the midpoints of two sides of a triangle. It does not necessarily have to be perpendicular or bisect the sides.