Triangle Angle Bisector Theorem

Front

What is the Triangle Angle Bisector Theorem?

Back

The Triangle Angle Bisector Theorem states that the angle bisector of an angle in 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 sides of lengths 8 and 6, and the angle bisector divides the opposite side into segments of lengths x and y, what is the relationship between x and y?

Back

x/y = 8/6 or x/y = 4/3.

Front

What is the formula to find the length of the angle bisector in a triangle?

Back

The length of the angle bisector can be calculated using 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

In triangle ABC, if AB = 10, AC = 6, and the angle bisector of angle A meets BC at D, what is the ratio BD:DC?

Back

The ratio BD:DC = AB:AC = 10:6 or 5:3.

Front

What is the significance of the angle bisector in triangle geometry?

Back

The angle bisector helps in determining the proportional lengths of the sides opposite to the angles, which is crucial for solving various geometric problems.

Front

If the angle bisector divides the opposite side into segments of 14 and 6, what are the lengths of the other two sides?

Back

The lengths of the other two sides can be found using the ratio 14:6, which corresponds to the lengths of the sides adjacent to the angle.

Front

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

Back

The angle bisector of a triangle intersects at a point called the incenter, which is the center of the circle inscribed within the triangle.

Front

How can the Triangle Angle Bisector Theorem be applied to find missing lengths in a triangle?

Back

By using the theorem, you can set up a proportion based on the lengths of the sides and the segments created by the angle bisector to solve for the missing lengths.

Front

What is the definition of an angle bisector?

Back

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

Front

If the lengths of the sides of a triangle are 12, 16, and 20, what is the angle bisector's effect on the opposite side?

Back

The angle bisector will divide the opposite side into segments that are proportional to the lengths of the sides 12 and 16.