Select the postulate that proves this fact. if g and h are different points in plane r, then a third point exists in r not on . postulate 1: a line contains at least two points. postulate 1a: a plane contains at least three points not all on one line. postulate 1b: space contains at least four points not all on one plane. postulate 2: through any two different points, exactly one line exists. postulate 3: through any three points that are not one line, exactly one plane exists. postulate 4: if two points lie in a plane, the line containing them lies in that plane. postulate 5: if two planes intersect, then their intersection is a line.

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality