Bisectors In Triangles

Front

What is a bisector in a triangle?

Back

A bisector in a triangle is a line segment that divides an angle into two equal parts.

Front

What is the Angle Bisector Theorem?

Back

The Angle Bisector Theorem states that the ratio of the lengths of the two segments created by an angle bisector on the opposite side is equal to the ratio of the lengths of the other two sides of the triangle.

Front

If a triangle has sides of lengths 7, 24, and 25, what type of triangle is it?

Back

It is a right triangle, as it satisfies the Pythagorean theorem (7^2 + 24^2 = 25^2).

Front

What is the definition of an altitude in a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

Front

How do you find the length of a bisector in a triangle?

Back

The length of a bisector can be found using the formula: l = √(ab(1 - c²/(a+b)²)), where a and b are the lengths of the sides adjacent to the angle, and c is the length of the opposite side.

Front

What is the relationship between the incenter and the angle bisectors of a triangle?

Back

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

Front

What is the definition of a median in a triangle?

Back

A median is a line segment joining a vertex to the midpoint of the opposite side.

Front

How many angle bisectors does a triangle have?

Back

A triangle has three angle bisectors, one for each angle.

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, and it is the center of the circumcircle.

Front

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

Back

The centroid is the point where the three medians of a triangle intersect, and it divides each median into a ratio of 2:1.