Given: In triangle ABC, ∠B ≅ ∠C Prove: AB ≅ ACTriangle A B C is shown. Angles A B C and B C A are congruent.

Complete the paragraph proof.

We are given that ∠B ≅ ∠C. Assume segment AB is not congruent to
.

If AB > AC, then m∠C > m∠B by the
. If AB < AC, then m∠C < m∠B by the converse of the triangle parts relationship theorem.

But by the definition of congruent, we know the measure of angle B equals the measure of
by the given statement. Therefore, we have a contradiction: AB = AC, and AB ≅ AC.

The suare root of 9x plus 7 plus the square rot of 2x equall to 7

Adesigner charges a one time fee of $200 plus $40 an hour for each project. write an expression to represent how much money the designer will make for a project

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )