Consider the diagram and proof by contradiction. Given: △ABC with ∠B ≅ ∠C
Prove: AB ≅ AC

Triangle A B C is shown. Angles A B C and B C A are congruent.

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

For the equations below which statement is true ?

For which pair of functions is (gof)(a)=|a|-2?

Finally, the arena decides to offer advertising space on the jerseys of the arena’s own amateur volley ball team. the arena wants the probability of being shortlisted to be 0.14. what is this as a percentage and a fraction? what is the probability of not being shortlisted? give your answer as a decimal. those shortlisted are entered into a final game of chance. there are six balls in a bag (2 blue balls, 2 green balls and 2 golden balls). to win, a company needs to take out two golden balls. the first ball is not replaced. what is the probability of any company winning advertising space on their volley ball team jerseys?