Exploring the Angle Bisector Theorem in Triangles

The video tutorial explains the angle bisector theorem and demonstrates its application through two example problems. In the first example, the theorem is used to find the unknown length x in a triangle, revealing it to be isosceles. The second example involves setting up and solving for x in another triangle using the same theorem. The tutorial emphasizes the use of ratios and cross-multiplication to solve these geometric problems.

What theorem is being used in the examples?

• Sine Rule

• Cosine Rule

• Angle Bisector Theorem

• Pythagorean Theorem

In the first triangle, what are the given lengths of the sides?

• 3 and 5

• 2 and 3

• 3 and 6

• 2 and 6

What is the length of the segment from the vertex to the angle bisector in the first triangle?

• 4

• 6

• 2

• 3

What is the value of x in the first triangle after solving the equation?

• 2

• 6

• 3

• 4

What type of triangle is the first triangle after solving for x?

• Scalene

• Right-angled

• Equilateral

• Isosceles

In the second triangle, what are the given lengths of the sides?

• 6 and 10

• 7 and 10

• 5 and 10

• 5 and 7

What is the total length of the side opposite the angle bisector in the second triangle?

• 12

• 10

• 7

• 5

What is the equation set up to solve for x in the second triangle?

• 5/(10 - x) = 7/(10 - x)

• 5/(10 - x) = 7/x

• 5/x = 7/(10 - x)

• 5/x = 7/x

What is the value of x in the second triangle after solving the equation?

• 7 and 1/6

• 6 and 1/6

• 5 and 1/6

• 4 and 1/6

What is the remaining segment length in the second triangle after solving for x?

• 4 and 5/6

• 5 and 5/6

• 7 and 5/6

• 6 and 5/6