SOLUTION: given triangle AKC is isoceles with segment KA is congruent to KC segment KB bisects angle AKC prove that angle A is congruent to angle C

Question 1171681: given triangle AKC is isoceles with segment KA is congruent to KC
segment KB bisects angle AKC
prove that angle A is congruent to angle C
Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.

Compare triangles AKC and CKA (the order of vertices is IMPORTANT (!) ).

These triangles have two pairs of congruent sides:

            the side AK of triangle AKC is congruent to side CK of triangle CKA,
    and
            the side CK of triangle AKC is congruent to side AK of triangle CKA.

In addition, these triangles have common angle K between these pairs of sides.

THEREFORE, according to SAS-test, these triangles are congruent.

Hence, their corresponding angles A and C are congruent.

At this point, the proof is completed.

RELATED QUESTIONS
Given: segment FD bisects angle EFC segment FC bisects angle DFB Prove: angle one is... (answered by ikleyn)

Given KQ is congruent to QA, QV bisects angle KQA, prove KB is congruent to... (answered by ikleyn)

how to solve this proof given: segment ab is congruent to segment cb, angle a is... (answered by richard1234)

Given: trianle MGR is an isoceles triangle with vertex angle MGR K is the midpoint of... (answered by venugopalramana)

Given: segment BA congruent to segment BC, Ray BD bisects angle ABC Prove: D is the... (answered by solver91311)

Ca you solve this proof? Given: angle V is congruent to angle Y, segment WZ bisects angle (answered by kingme18)

Given: L is the midpoint of line segment IE, line segment NE is congruent to NI. Prove... (answered by solver91311)

what would be the steps to solve the proof with the given: segment ab is congruent to... (answered by ikleyn)

Given: Quadrilateral ABCD Segment AC bisects angle DAB Segment DB bisects angle ADC... (answered by math_tutor2020)