Points of Concurrency review

What is the orthocenter of a triangle?

• The point where the three altitudes of the triangle intersect.

• The center of the triangle's circumcircle.

• The midpoint of the triangle's longest side.

• The point where the medians of the triangle intersect.

What is an altitude in a triangle?

• A line segment connecting the midpoints of two sides.

• A perpendicular segment from a vertex to the line containing the opposite side.

• The longest side of the triangle.

• An angle formed by two sides of the triangle.

What is the difference between a median and an altitude?

• A median connects a vertex to the midpoint of the opposite side, while an altitude is perpendicular to the opposite side.

• A median is always longer than an altitude in any triangle.

• An altitude can only be drawn in right triangles, while a median can be drawn in all triangles.

• A median divides a triangle into two equal areas, while an altitude does not.

What is a point of concurrency in geometry?

• A point where two lines intersect.

• A point where three or more lines intersect.

• A point where lines are parallel.

• A point where lines are perpendicular.

What is the relationship between the centroid and the triangle's area?

• The centroid is the point where all three medians intersect, and it does not affect the area of the triangle.

• The centroid divides each median into two segments, one of which is twice the length of the other, affecting the triangle's area calculations.

• The centroid is located at the midpoint of the triangle's base, which determines the area.

• The centroid is the vertex of the triangle that contributes the most to the area.

What is the significance of the circumcenter in triangle construction?

• It helps in constructing the circumcircle, which is essential for various geometric constructions.

• It determines the area of the triangle.

• It is the point where the altitudes of the triangle intersect.

• It is the midpoint of the longest side of the triangle.

Can the circumcenter be located outside the triangle?

• No, it is always inside the triangle.

• Yes, in the case of obtuse triangles, the circumcenter lies outside the triangle.

• Yes, but only in right triangles.

• It can be inside or outside depending on the triangle's angles.

Name the three main points of concurrency in a triangle.

• Centroid, circumcenter, and orthocenter.

• Incenter, centroid, and excenter.

• Circumcenter, orthocenter, and centroid.

• Centroid, circumradius, and orthocenter.

What is the centroid of a triangle?

• The point where the three medians of the triangle intersect.

• The point where the three altitudes of the triangle intersect.

• The point where the three sides of the triangle are equal.

• The point where the triangle's area is maximized.

What is a median in a triangle?

• A segment that connects a vertex to the midpoint of the opposite side.

• A line that bisects an angle of the triangle.

• A segment that connects two midpoints of the sides of the triangle.

• A line that extends from a vertex to the opposite side without touching it.