The figure below shows a quadrilateral ABCD. Sides AB and DC are equal and parallel: A quadrilateral ABCD is shown with the opposite sides AB and DC shown parallel and equal.

A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram:

Side AB is parallel to side DC, so the alternate interior angles, angle ABD and angle CDB, are congruent. Side AB is equal to side DC, and DB is the side common to triangles ABD and CDB. Therefore, the triangles ABD and CDB are congruent by SAS postulate. By CPCTC, angles DBC and BDA are congruent and sides AD and BC are congruent. Angle DBC and angle BDA form a pair of vertical angles that are congruent. Therefore, AD is parallel and equal to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.

Which statement best describes a flaw in the student's proof?

Triangles ABD and BCD are congruent by the SSS postulate instead of the SAS postulate.
Triangles ABD and BCD are congruent by the AAS postulate instead of the SAS postulate.
Angle DBC and angle BDA form a pair of corresponding angles, not a pair of vertical angles.
Angle DBC and angle BDA form a pair of alternate interior angles that are congruent, not a pair of vertical angles.

7.(03.01 lc)which set represents the range of the function shown? {(-1, 5), (2,8), (5, 3), 13, -4)} (5 points){-1, 2, 5, 13){(5, -1), (8, 2), (3,5), (-4, 13)){-4, 3, 5, 8}{-4, -1, 2, 3, 5, 5, 8, 13}

What could explain what happened when the time was equal to 120 minutes

You and three friends will be going out to eat at your favorite restaurant! each of you will order three items of your choice. you will also need to leave a tip. if you split the bill evenly among all four of you, how much will each person need to contribute? locate a menu for your favorite restaurant and pick three items for yourself and each friend. list the restaurant name, items, and prices in a table like the one below. in the column labeled subtotal, determine the cost of each person’s order. the customary tip is 20% of the total bill. in the column labeled tip, calculate the amount of tip each person should leave. in the column labeled total bill, determine the total of each person’s order, including the tip. restaurant name: names item 1 price item 2 price item 3 price subtotal tip total bill your name friend #1 friend #2 friend #3 part 2: questions answer the following questions, showing all work: what is the total cost of the entire bill (all four meals), including tip? write an expression using fractions to show how to determine the amount that each person will pay. then calculate each person's contributions showing all steps in long division. if each person paid an equal amount, who would save the most money? explain your reasoning using at least two complete sentences.