Consider the diagram and proof by contradiction.
given: △abc with ∠b ≅ ∠c
prove: ab ≅ ac
it is given that ∠b ≅ ∠c. assume ab and ac are not congruent. if ab > ac, then m∠c > m∠b by if ac > ab, then m∠b > m∠c for the same reason. however, using the given statement and the definition of congruency, we know that m∠b = m∠c. therefore, ab = ac and ab ≅ ac.
what is the missing reason in the proof?
converse of the triangle parts relationship theorem
substitution
definition of congruency
converse of the isosceles triangle theorem

At river bank, checking account customers earn 0.75% interest a month on their account balances, pay no service fees for writing checks, and pay a monthly $2.00 financial charge. calculate the income earned in one month on the checking account for a customer with an account balance of $1,000. a. $4.25 b. $5.50 c. $6.75 d. $7.25 checking account earnings at baker’s bank are expressed by the equation: i = -0.09x + 10.2. while the earnings at elite bank are modeled by: i = -0.02x + 7.5. in both cases, x is the number of checks written. at what number of checks will elite bank start generating more checking account income than baker's bank? a. 12 b. 25 c. 39 d. 42 emilio’s checking account had a balance of 728.32 at the beginning of the week. he wrote checks for the following amounts throughout the week: $99.48, $33.50, $18.23, and $72.05. he also deposited his paycheck in the amount of $1,109.90. what is his account balance at the end of the week? a. $1,192.35 b. $1,222.86 c. $1,540.52 d. $1,614.96