The Springfield Middle School sixth-grade teachers of history, science, and art are listed in the table.

Sixth Grade Teachers
History
Science
Art
Mr. Nelson
Ms. Porter
Mr. Rosenberger
Ms. Hogan
Mr. Grist
Ms. Patel
Ms. Miller
Ms. O’Reilly
Ms. George
Mr. Springer
Ms. Trufant
Ms. Callahan
Ms. Daniels
Mr. Pollard

Ms. Cartwright
Ms. Davis

Mr. Bergeron
Mr. Cooper

Mr. Chin
Mr. Dawson

Ms. Sarno

How many combinations of one history, one science teacher, and one art teacher include Mr. Bergeron?
13
36
252
288

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)