In parallelogram QRST QS RT Is QRST a rectangle ?
2 answers:
Answer:
The correct option is A.
Step-by-step explanation:
It is given that the QRST is a parallelogram and the diagonals QS and RT are congruent.
According to the property of parallelogram if the length of diagonals are same, then the parallelogram is rectangle. We can also prove it.
Let QRST be an parallelogram and QS=RT.
In triangles QRT and RQS.
(Diagonals)
(Common side)
(Opposite sides of the parallelogram are same)
So by SSS rule of congruence, triangle QRT and triangle RQS are congruent.
By CPCT,
Since the sum of two consecutive angles of a parallelogram is 180 degree.
Therefore the measure of angle R and angle Q are 90 degree.
Similarly in triangle QST and RTS,
(Diagonals)
(Common side)
(Opposite sides of the parallelogram are same)
So by SSS rule of congruence, triangle QST and RTS are congruent.
By CPCT,
Since the sum of two consecutive angles of a parallelogram is 180 degree.
Therefore the measure of angle S and angle T are 90 degree.
Since the measure of all interior angles of QRST are 90 degree, therefore the parallelogram QRST is a rectangle.
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The first thing you have to do is study the graph. The two functions are
f(x) = 4^x That's the curved graph. (in red)
g(x) = x + 4. That's the straight line. (in blue)
You know that the first one is not a linear relationship because the x values go from integer values -2 to 2 (including 0). The y values are a bit different. They go from 1/16 to 16 with those integer values. So you could try y = 4^(-x). It doesn't work, but you could try it. It gives the table numbers for y in the reverse order that the table you are given goes. For x you get -2 -1 0 1 2 and for y you would get 16 4 1 1/4 1/16.
You could try y = (1/4)^x
For this try, you would get x = -2 -1 0 1 2 and for y = 16 4 0 1/4 and 1/16
but that doesn't work either.
You could try until you get y = 4^x which does work.
g(x) is a lot easier to deal with. It looks better behaved. as x goes up, so does y. You will find that the y values obey y = x + 4. You could try other lines, but that one works. Many times it's just a guess
The first thing you have to do is study the graph. The two functions are
f(x) = 4^x That's the curved graph. (in red)
g(x) = x + 4. That's the straight line. (in blue)
You know that the first one is not a linear relationship because the x values go from integer values -2 to 2 (including 0). The y values are a bit different. They go from 1/16 to 16 with those integer values. So you could try y = 4^(-x). It doesn't work, but you could try it. It gives the table numbers for y in the reverse order that the table you are given goes. For x you get -2 -1 0 1 2 and for y you would get 16 4 1 1/4 1/16.
You could try y = (1/4)^x
For this try, you would get x = -2 -1 0 1 2 and for y = 16 4 0 1/4 and 1/16
but that doesn't work either.
You could try until you get y = 4^x which does work.
g(x) is a lot easier to deal with. It looks better behaved. as x goes up, so does y. You will find that the y values obey y = x + 4. You could try other lines, but that one works. Many times it's just a guess