Topic 5 Relationships in Triangles

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is equidistant from all three vertices of the triangle.

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 gravity and divides each median into a ratio of 2:1.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the three altitudes of a triangle intersect. Its position varies depending on the type of triangle (acute, right, or obtuse).

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

How do you find the circumradius of a triangle?

Back

The circumradius (R) can be found using the formula R = (abc)/(4K), where a, b, and c are the lengths of the sides of the triangle and K is the area of the triangle.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.

Front

What is the relationship between the centroid and the medians of a triangle?

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.

Front

What is the area of a triangle given its base and height?

Back

The area (A) of a triangle can be calculated using the formula A = (1/2) * base * height.

Front

What is the significance of the circumcenter in a triangle?

Back

The circumcenter is significant because it is the center of the circumcircle, which is the circle that passes through all three vertices of the triangle.

Front

What is the relationship between the orthocenter and the triangle's altitudes?

Back

The orthocenter is the point where all three altitudes of a triangle intersect, and it can be located inside, on, or outside the triangle depending on the triangle's type.