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
The investigating team suspected that there were differences in the cost of repairing cars in workshop i and workshop ii. the investigating team suspected that the costs raised by workshop i were greater than workshop ii. for that they tested the repair of 15 cars in each workshop to see the cost of repairs. the decision of the right hypothesis to prove the suspicion above is a. h0 : μ1- μ2 = 0; ha : μ1- μ2 ≠ 0 b. h0 : μ1- μ2 ≥ 0; ha : μ1- μ2 < 0 c. h0 : μd ≥ 0; ha : μd < 0 with μd = μ2- μ1 d. h0 : μd = 0; ha : μd ≠ 0 with μd = μ2- μ1 e. h0 : μ1- μ2 = 0; ha : μ1- μ2 ≥ 0