Exploring the Angle Bisector Theorem

The video tutorial explores the angle bisector theorem, explaining how it divides a triangle into proportional segments. It provides two examples to demonstrate how to apply the theorem to solve for missing lengths in triangles. The first example involves setting up a proportion to find the length of a side, while the second example requires more complex problem-solving to determine segment lengths. The tutorial emphasizes understanding the relationships between triangle sides and using proportions effectively.

What is the initial setup of the triangle in the Angle Bisector Theorem?

• Triangle DEF with angle bisector EF

• Triangle XYZ with angle bisector YW

• Triangle GHI with angle bisector HI

• Triangle ABC with angle bisector CD

What does the angle bisector do to the triangle?

• Splits the triangle into two congruent triangles

• Splits the triangle into proportional segments

• Splits the triangle into two equal areas

• Splits the triangle into two right triangles

Which proportion can be derived from the angle bisector theorem?

• AD/DB = AC/CB

• AD/DB = AB/BC

• AD/AC = DB/CB

• AD/AC = AB/BC

What does the proportion AD/DB = AC/CB compare?

• Left and right sides of AB and BC

• Left and right sides of AB and AC

• Left and right sides of AC and CB

• Left and right sides of AB and CB

In the first example problem, what is the length of XY?

• 2

• 5

• 7

• 3

In the first example problem, what is the length of XW?

• 7

• 5

• 3

• 2

In the first example problem, what is the length of XZ?

• 16/3

• 5

• 7

• 3

In the second example problem, what is the total length of XZ?

• 3

• 4

• 5

• 7

In the second example problem, what is the length of XW?

• 4

• 5

• 3

• 15/7

In the second example problem, what is the length of WZ?

• 20/7

• 3

• 4

• 5