Angle Bisectors - Triangles

Front

What is an angle bisector?

Back

An angle bisector is a line or ray that divides an angle into two equal parts.

Front

In a triangle, how many angle bisectors can be drawn?

Back

Three angle bisectors can be drawn, one from each vertex of the triangle.

Front

What is the property of angle bisectors in a triangle?

Back

The angle bisector of a triangle divides the opposite side into two segments that are proportional to the lengths of the other two sides.

Front

If a triangle has angles of 30°, 60°, and 90°, what are the measures of the angles formed by the angle bisectors?

Back

The angle bisectors will create angles of 15°, 30°, and 45° respectively.

Front

What is the relationship between the angle bisector and the opposite side in a triangle?

Back

The angle bisector divides the opposite side into two segments that are proportional to the adjacent sides.

Front

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

Back

Use the formula: l = (2ab)/(a+b) * cos(C/2), where a and b are the lengths of the sides adjacent to the angle, and C is the angle.

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 the angle bisector on the opposite side is equal to the ratio of the lengths of the other two sides.

Front

If one angle of a triangle is 80°, what is the measure of the angle formed by its angle bisector?

Back

The angle formed by the angle bisector will be 40°.

Front

In triangle ABC, if AB = 6, AC = 8, and the angle bisector of angle A meets BC at D, what is the ratio BD:DC?

Back

The ratio BD:DC = AB:AC = 6:8 or 3:4.

Front

What is the significance of the incenter in relation to angle bisectors?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is the center of the inscribed circle.