Geo: topic 3- parallelograms 1pt a rhombus is a parallelogram with all four sides of equal length. one way to determine if a given parallelogram is a rhombus is to test whether its diagonals are perpendicular. the vertices of a parallelogram are m(−1,2), n(9,2), p(3,−6), and q(−7,−6). determine whether the parallelogram is a rhombus by checking to see if the diagonals are perpendicular. what is the slope of mp¯¯¯¯¯¯? what is the slope of nq¯¯¯¯¯¯? are diagonals mp¯¯¯¯¯¯ and nq¯¯¯¯¯¯ perpendicular? is the parallelogram a rhombus?

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