Ted is picking one of his three children (ed, jed, or ned) to do the dishes.
what is a fair way to do this?
o
a. have each of the children wash one dish. the one who does the
best job gets to do the rest of the dishes.
o
b. toss a coin twice. if it comes up heads 2 times, pick ed. if it
comes up heads 1 time, choose jed. if it comes up heads 0 times,
choose ned.
o
c. roll a number cube. if an odd number comes up, pick ed. if a 2 or
a 4 comes up, pick jed. if any other number comes up, pick ned.
d. make a spinner with three equal-sized sections. assign each child
one section and spin the spinner. the child whose section comes
up does the dishes.

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