A General Note: Perfect Square Trinomials A perfect square trinomial can be written as the square of a binomial:
a2+2ab + b2=(a + b)2
and
a2-2ab +b2= (a - b)2
The factoring techniques of grouping or trial and error still work on perfect square trinomials
Given a perfect square trinomial, factor the trinomial into the square of a
binomial.
1. Confirm that the first term and third term are perfect squares.
2. Confirm the middle term is equal to 2ab.
3. Write the trinomial in the factored form (a + b)2or (a - b) 2 based upon
the sign of the middle term.

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)