SOLUTION: Directions: Set up and complete a proof of the statement. If a triangle is isosceles, the triangle formed by its base and the angle bisectors of its base angles is also isoscele

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Question 58347: Directions: Set up and complete a proof of the statement.
If a triangle is isosceles, the triangle formed by its base and the angle bisectors of its base angles is also isosceles.
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
Define:
Big Triangle: ABC where A is the top part, B is the bottom left, and C is the bottom right
Small Triangle: Top part is labled D
1. AB = AC; < ABC = < ACB ........ 1. given
2. 2 * < DBC = < ABC and 2 * < DCB = < ACB ..... 2. definition of angle bisector
3. 2 * < DBC = < ABC and 2 * < DCB = < ABC ..... 3. substitution
4. 2 * < DBC = 2 * < DCB ................. 4. transitive property
5. < DBC = < DCB ................... 5. division
6. DB = DC ....................... 6. opposite segements of congruent angles are congruent
7. triangle DBC is isoceles ...... 7. definition of isoceles triangles
I am sorry if it is quite long; I just like to make things clear.