1. The problem involves a triangle ABC with a point D on side AC.
2. Side AB is labeled 15, side BC is labeled 2x - 4, and side AC is labeled 18.
3. A line segment BD connects vertex B to point D on AC, and the length of DC is labeled 8.
4. Since D lies on AC, the length of AD can be found by subtracting DC from AC: AD = AC - DC = 18 - 8 = 10.
5. The red arc at angle ABD and angle CBD indicates that BD bisects angle ABC.
6. By the Angle Bisector Theorem, the ratio of the lengths of the two segments created on the opposite side (AC) is equal to the ratio of the other two sides of the triangle.
7. Therefore, AD/DC = AB/BC.
8. Substituting the known values: 10/8 = 15/(2x - 4).
9. Simplify the left side: 5/4 = 15/(2x - 4).
10. Cross-multiply: 5 * (2x - 4) = 4 * 15.
11. Expand: 10x - 20 = 60.
12. Add 20 to both sides: 10x = 80.
13. Divide by 10: x = 8.
Parent Tip: Review the logic above to help your child master the concept of triangle angle bisector theorem worksheet.
