GM-U5.1c Lesson Check: Angle Bisector Theorem

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, 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

How do you find the length of a segment created by an angle bisector?

Back

Use the formula: (a/b) = (c/d), where a and b are the lengths of the sides adjacent to the angle, and c and d are the lengths of the segments created on the opposite side.

Front

What is the significance of the Angle Bisector Theorem in solving triangle problems?

Back

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

Front

In triangle ABC, if AB = 10, AC = 15, and the angle bisector of angle A intersects BC at D, what is the ratio BD:DC?

Back

The ratio BD:DC is 10:15 or 2:3.

Front

What is a practical application of the Angle Bisector Theorem?

Back

It can be used in construction and design to ensure that angles are bisected accurately for aesthetic and structural purposes.

Front

If the lengths of two sides of a triangle are 12 and 16, what is the maximum possible length of the third side?

Back

The maximum possible length of the third side is 28 (12 + 16).

Front

What is the minimum possible length of the third side of a triangle with sides 12 and 16?

Back

The minimum possible length of the third side is 4 (16 - 12).

Front

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

Back

The lengths of the two adjacent sides are in the ratio 1:2.

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.