Given: δabc is a right triangle.
prove: a2 + b2 = c2

right triangle bca with sides of length a, b, and c. perpendicular cd forms right triangles bdc and cda. cd measures h units, bd measures y units, da measures x units.

the following two-column proof with missing justifications proves the pythagorean theorem using similar triangles:

statement justification
draw an altitude from point c to line segment ab
let segment bc = a
segment ca = b
segment ab = c
segment cd = h
segment db = y
segment ad = x
y + x = c
c over a equals a over y and c over b equals b over x
a2 = cy; b2 = cx
a2 + b2 = cy + b2
a2 + b2 = cy + cx
a2 + b2 = c(y + x)
a2 + b2 = c(c)
a2 + b2 = c2

which is not a justification for the proof?
pieces of right triangles similarity theorem
side-side-side similarity theorem
substitution
addition property of equality

Janice determined there were 10 possible outcomes when tossing two coins and spinning a spinner numbered 1 through 6. what is the correct number? what might have been janice's error?

*let m∠cob = 50°30’, m∠aob = 70° and m∠aoc = 20°30’. could point c be in the interior of ∠aob? why? a. point c could be the interior of aob but it is not the only case b. point c is the interior of aob c. point c is not the interior of aob d. the given is not possible for the plane geometry answer

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i. e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)