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netineya [11]
4 years ago
14

Which of the following statements can be used to prove quadrilateral QRST

Mathematics
1 answer:
baherus [9]4 years ago
7 0

QR || ST & QT=RS

That could be an isosceles trapezoid.  Don't check this one.

QR=ST & QR || ST

Congruent Parallel sides.  CHECK ME.

QT || RS & QR=ST.

Basically the same as the first, don't check.

QR=ST & QT=RS

Quadrilateral with equal opposite sides is a parallelogram.  CHECK ME

QR=ST & ST=ST

ST=ST is not news.  Congruent opposite sides.  Don't check me.

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Let s,\ m\, l be the short, medium and long side, respectively. If we translate all the information into formulas, we get the following system:

\begin{cases} l = 2s\\ m=s+3\\ s+m+l = 27 \end{cases}

Using the second equation, we can express the middle side in terms of the small one, and reduce the system to two equations in two unknowns:

\begin{cases} l = 2s\\ s+(s+3)+l = 27 \end{cases}

And thus

\begin{cases} l = 2s\\2s+l = 24 \end{cases}

But then again, using the first equation, the third becomes

2s+l = 24 \iff l+l = 24 \iff 2l = 24 \iff l=12

So, the longest side is 12. Since the small is half the long, we have s = 6. Finally, the medium is three more of the small, so we have m = 6+3 = 9

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4 years ago
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Answer:

Step-by-step explanation:

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