Question 159413
your plan is as follows:
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prove that CD is perpendicular to AB.
prove that angles opposite congruent sides of isosceles triangle are congruent.  assume this is previously proven. if not, you'll have to prove it yourself.  i'll provide that proof separately.
prove that the two right triangles created by the altitude are congruent.
prove that angles created by altitude are equal to each other.
prove that they bisect the angle.
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proof that angles opposite congruent sides of isosceles triangle are congruent
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triangle ABC is isosceles and AC = CB (given)
draw CD to intersect AB so that AD = DB (construction)
triangle ADC congruent to triangle BDC by SSS (AC = CB is given, CD = CD by reflexive property of equality (anything is equal to itself), AD = DB by construction)
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your main proof.
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CD is perpendicular to AD (this is by definition of the altitude of a triangle)
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angle CAD congruent to angle CBD (opposite angles of an isosceles triangle are equal).  just stating it should be enough but if they want proof, it is up above.
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triangle CDA is congruent to CDB (SSA - two triangle are congruent if two corresponding sides and an angle not between them are congruent.  this is a basic postulate of congruent triangles.  corresponding sides are CA congruent to CB, CD congruent to CD, corresponding angles are CAD congruent to CBD)
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angle ACD = angle BCD (corresponding angles of congruent triangles are congruent)
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CD bisects angle ACB (by definition the bisector of an angle creates two equal angles formed by the bisector)