Prove that the angle bisectors of the base of the isosceles angles of the isosceles triangle are congruent using statement and reason proof
i dont really now how to prove this problem but i now what a transversal is and the angles of a trashes line. can u guys plz solve and explain a the bottom how u did it it would be a real help thanks
google is your friend. Try this:
https://www.algebra.com/algebra/homework/word/geometry/Angle-bisectors-in-an-isosceles-triangle.lesson
thanks :) :D
To prove that the angle bisectors of the base of the isosceles angles of an isosceles triangle are congruent, we can use the Angle Bisector Theorem.
Here's how we can prove it step by step:
Statement 1: Let ABC be an isosceles triangle with AB = AC.
Reason 1: Given information.
Statement 2: Let AD and AE be the angle bisectors of angles B and C, respectively.
Reason 2: Construction.
Statement 3: Angle BAD = angle CAE.
Reason 3: By definition, the angle bisectors of angles B and C divide angles B and C equally.
Statement 4: Triangle ABD is congruent to triangle ACE.
Reason 4: By the Angle-Side-Angle (ASA) congruence criterion.
Explanation: We have angle BAD = angle CAE (Statement 3), AB = AC (Given), and angle A is common to both triangles.
Statement 5: BD = CE.
Reason 5: Corresponding parts of congruent triangles are congruent (CPCTC).
Therefore, the angle bisectors of the base of the isosceles angles of an isosceles triangle are congruent, as shown by the congruent triangles ABD and ACE.