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3 years ago

Which theorem proves ABC=DCB? Why?

Mathematics

1 answer:

Akimi4 [234]3 years ago

7 0

Answer:

Parallel postulate : ALTERNATE INTERIOR ANGLES THEOREM.

Step-by-step explanation:

ALTERNATE INTERIOR ANGLES THEOREM : if a transversal cuts 2 parallel lines, then the alternate interior angles are said to be congruent.

( alternate interior angles : in the given figure, DCB and ABC are alternate interior angles.

ACB and CBD are another pair of alternate interior angles.)

[ theorem is an accepted truth or a verified correct statement already i.e, take protractor and measure it will be same in EVERY case. though i have provided the proof below..]

PROOF: since we know that vertically opposite angles will be congruent, so the angle vertically opposite to DCB will be same as DCB. ( refer attachment for vertically opposite angles) now, as corresponding angles will be congruent (see attachment to know what are corresponding angles), the angle vertically opposite to DCB and ABC are corresponding angles. therefore DCB and ABC are also equal

hence, ABC=DCB.

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3 years ago

Anita purchased a couch that was priced at $700. She will also have to pay 6% sales tax. How much will she pay in total for the

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Step-by-step explanation:

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2 years ago

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Oduvanchick [21]

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3 years ago

Solve the system using substitution.<br> 2x = 5y + 14<br> x = 5y

andrew-mc [135]

Answer:

Step-by-step explanation:

To solve an equation, we can only have one variable. In this case, we are given the system 2x = 5y + 14. However, we are given the value of x in terms of y. We can substitute 10y in for 2x and solve.

10y = 5y + 14

First, we need to get all the variables on one side of the equation, so we subtract 5y.

5y = 14

Divide by 5

y = 14/5 or 2 4/5 or 2.8

Now for the x part.

2x = x + 14

Subtract 1x

x = 14

Now we check our answer.

2(14) = 5(2.8) + 14

28 = 14 + 14

28 = 28

Because 28 equals 28, our solutions are correct.

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3 years ago