Review Special Segments in Triangles

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side.

Front

What is the point of concurrency of the medians called?

Back

The point of concurrency of the medians is called the centroid.

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.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is the center of the triangle's incircle.

Front

What is the orthocenter of a triangle?

Back

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

Front

In which type of triangle can the orthocenter be located outside the triangle?

Back

The orthocenter can be outside the triangle if the triangle is obtuse.

Front

If m∠GCD = 3x + 8 and m∠DCF = 5x - 4, how do you find the value of x?

Back

Set the two expressions equal to each other and solve for x: 3x + 8 = 5x - 4.

Front

What is the relationship between the lengths of the segments created by a median in a triangle?

Back

A median divides the triangle into two smaller triangles of equal area.

Front

What is the formula for finding the length of a median in a triangle?

Back

The length of a median can be calculated using the formula: m = 1/2 * √(2a² + 2b² - c²), where a and b are the lengths of the sides adjacent to the median, and c is the length of the side opposite the median.

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the center of mass of the triangle and divides each median into a ratio of 2:1.