if two sides of one triangle are congruent to two sides of another triangle, then the third side of the triangle with the larger included angle is longer.GA congruent to GB angle A congruent to angle B AX congruent to YB GX congruent to GY triangle XGY is isosceles GX congruent to GY AX congruent to XY angles GXY and GYX are acute (base angles of an isosceles triangle) angle GXA is obtuse (supplementary to an acute angle) GA > GX (by the SAS inequality theorem. GA > GY (since GX is congruent to GY <-----------STEP M For contradiction, assume angle XGY congruent to angle XGA Extend GX to twice its length to E such that GX congruent to EX. Draw YE AX congruent to XY (given) GX congruent to EX (by construction) angle GXA congruent to angle EXY (vertical angles are congruent) triangle GAX and triangle EYX are congruent by SAS GA congruent to EY (c.p.c.t) <----------------- STEP N angle XGA congruent to angle YEX (c.p.c.t.) angle YEX congruent to angle XGY Triangle GYE is isosceles (base angles congruent) GY congruent to EY (c.p.c.t) <------------------ STEP P From steps N and P above, GA is congruent to GY <----------------- Step Q Step Q contradicts Step M. Therefore, the assumption that angle XGY congruent to angle XGA is false, so the student did not trisect angle AGB. Edwin