Look at the quadrilateral shown below: melissa writes the following proof for the theorem: if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram: melissa's proof 1. for triangles aob and cod, angle 1 is equal to angle 2 as they are vertical angles. 2. ao = oc and bo = od because it is given that diagonals bisect each other. 3. the are congruent by sas postulate. 4. similarly, triangles aod and cob are congruent. 5. by cpctc, ab is equal to dc. 6. by cpctc, ad is equal to bc. 7. as the opposite sides are congruent the quadrilateral abcd is a parallelogram. which is the missing phrase in melissa's proof? a: angles adb and cbd b: (my guess) angles aob and cod c: triangles adb and cbd d: triangles aob and cod

answer: the missing part will ab and cd are congruent by sas postulate.

explanation: according to the question here, a quadrilateral abcd in which o is the point at which the diagonals ac and bd cut each other. and, and are the angles of triangles aob and cod respectively.

now the theorem is " if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram"

so, according to melissa's proof- for triangles aob and cod, angle 1 is equal to angle 2 as they are vertical angles.

ao = oc and bo = od because it is given that diagonals bisect each other.

the ab and cd are congruent by sas postulates.

similarly, triangles aod and cob are congruent.  

by cpctc, ab is equal to dc.  

by cpctc, ad is equal to bc.  

as the opposite sides are congruent the quadrilateral abcd is a parallelogram.

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt

113.1

step-by-step explanation:

v=4

3πr3=4

3·π·33≈113.09734