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

Front

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

Back

Use the formula: length of angle bisector = √(ab(1 - c²/(a+b)²)), where a and b are the lengths of the sides forming the angle, and c is the length of the opposite side.

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 and is crucial for solving various geometric problems involving triangles.

Front

If the lengths of two sides of a triangle are 10 and 15, what is the maximum possible length of the third side?

Back

The maximum possible length of the third side is 24 (10 + 15 - 1).

Front

What is the relationship between the angles and sides in a triangle?

Back

In a triangle, the larger angle is opposite the longer side, and the smaller angle is opposite the shorter side.

Front

If a triangle has angles of 30°, 60°, and 90°, what are the ratios of the sides?

Back

The ratios of the sides opposite these angles are 1:√3:2.

Front

What is the sum of the interior angles of a triangle?

Back

The sum of the interior angles of a triangle is always 180°.

Front

How can you determine if three lengths can form a triangle?

Back

Use the triangle inequality theorem: the sum of the lengths of any two sides must be greater than the length of the third side.

Front

What is an exterior angle of a triangle?

Back

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.