Proving the Single Opposite Side Pair Theorem Given: AD=BC and AD BC prove:ABCD is a parallelogram

8 parts

Step-by-step explanation:

1. AD≅BC                                                                Given

2. AD║BC                                                                Given

3. ∠DAC and ∠BCA                                                Def. of alt.

are alt. interior  angles                                          interior angle

4. ∠DAC ≅ ∠BCA                                           alternate interior angle theorem

5. AC ≅ AC                                                       reflexive property

6. ΔDAC ≅ ΔBCA                                                     SAS

7. AB ≅ CD                                                              CPCTC

8. ABCD is a parallelogram                                parallelogram side theorem

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation:

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.