The triangles shown are congruent by the SSS congruence theorem. 3 rigid transformations are shown. Triangle A B C is first rotated about point C to form triangle A prime B prime C. Triangle A prime B prime C is then shifted down to form triangle A double-prime B double-prime C prime. Triangle A double-prime B double-prime C prime is reflected across A double-prime B double-prime to form triangle A double-prime B double-prime C double-prime

The diagram shows the sequence of three rigid transformations used to map TriangleABC onto TriangleA"B"C". What is the sequence of the transformations?

rotation, then reflection, then translation
rotation, then translation, then reflection
translation, then reflection, then rotation
translation, then rotation, then reflection

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