Angle Bisector Theorem Practice IRR

Front

What is the Angle Bisector Theorem?

Back

The 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 length x and y, what is the relationship between x and y?

Back

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

Front

Find the missing length if the angle bisector divides the opposite side into segments of 15 and x, with the other two sides being 9 and 12.

Back

x = 20.

Front

Solve for x if the angle bisector divides the opposite side into segments of 10 and x, with the other two sides being 5 and 8.

Back

x = 16.

Front

What is the value of the missing segment if the angle bisector divides the opposite side into segments of 12 and x, with the other two sides being 3 and 4?

Back

x = 16.

Front

What is the value of the missing segment if the angle bisector divides the opposite side into segments of 8 and x, with the other two sides being 2 and 3?

Back

x = 12.

Front

If the lengths of the two segments created by the angle bisector are 4 and 6, what are the lengths of the two sides of the triangle?

Back

The lengths of the two sides are in the ratio 2:3.

Front

What is the formula to find the length of the segment created by the angle bisector?

Back

The length of the segment can be found using the formula: (a*b)/(a+b) where a and b are the lengths of the two sides.

Front

If the angle bisector divides the opposite side into segments of 5 and 10, what is the ratio of the lengths of the two sides?

Back

The ratio is 1:2.

Front

What is the significance of the Angle Bisector Theorem in triangle geometry?

Back

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