Triangles T S R and Q R S overlap at point P. Angle S T R is 66 degrees and angle S Q R is 66 degrees. The lengths of T S and Q R are both 5 inches. Can ΔTSR and ΔQRS be proven congruent by SAS? yes, because along with the given information on the diagram, SR ≅ RS by the reflexive property yes, because a reflection will map ΔTSR onto ΔQRS yes, because P appears to be the midpoint of SQ and TR no, because not enough is information given to prove the triangles congruent by SAS

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