Q2 -Homework 3 - Center of Triangles Review

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is also known as the center of mass or balance point of the triangle.

Front

What are medians in a triangle?

Back

Medians are line segments that connect a vertex of a triangle to the midpoint of the opposite side.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the three perpendicular bisectors of a triangle intersect. It is the center of the circumcircle, which passes through all three vertices.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the three angle bisectors of a triangle intersect. It is the center of the incircle, which is tangent to all three sides.

Front

What are angle bisectors in a triangle?

Back

Angle bisectors are line segments that divide an angle into two equal parts.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the three altitudes of a triangle intersect.

Front

What are altitudes in a triangle?

Back

Altitudes are line segments drawn from a vertex of a triangle perpendicular to the opposite side.

Front

If m∠CAP = 34°, what is ∠CAB?

Back

∠CAB = 68°.

Front

What is the relationship between the centroid and the medians?

Back

The centroid divides each median into two segments, with the segment connecting the vertex to the centroid being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Front

How do you find the circumcenter of a triangle?

Back

To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle. The point where they intersect is the circumcenter.