Match the reasons with the statements given.
given:
1 = 2
5 = 6
prove:
mq = mp
1. ∠3, ∠5 are supplementary and ∠4, ∠6 are supplementary
2. ∠5 = ∠6 and ∠1 = ∠2
3. ∠3 = ∠4
4. mn = mn
5. triangle mnq congruent to triangle mnp
6. mq = mp
a. cpcte
b. given
c. exterior sides in opposite rays.
d. asa
e. reflexive
f. supplements to = angles.

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