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, what is the ratio of the segments created by the angle bisector on the opposite side?

Back

The ratio of the segments is 8:6 or 4:3.

Front

What is an angle bisector?

Back

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

Front

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

Back

The length of the angle 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 significance of the Triangle Angle Bisector Theorem in solving problems?

Back

It helps in finding unknown lengths in triangles and establishing relationships between the sides of the triangle.

Front

If the lengths of two sides of a triangle are 10 and 15, what is the length of the segment created by the angle bisector on the opposite side if the opposite side is 25?

Back

The segment lengths are in the ratio 10:15, which simplifies to 2:3. Therefore, the segments are 10 and 15.

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 lengths of the other two sides.

Front

Can the Triangle Angle Bisector Theorem be applied to non-triangular shapes?

Back

No, the Triangle Angle Bisector Theorem specifically applies to triangles.

Front

What is the formula for the angle bisector length in terms of the sides of the triangle?

Back

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

If a triangle has sides of lengths 7, 24, and 25, what is the ratio of the segments created by the angle bisector of the angle opposite the side of length 25?

Back

The ratio is 7:24.