Consider a parallelogram in which one side is 3 inches long, another side measures 4 inches, and the measurement of one angle is
1 answer:
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Answer:
(a) one parallelogram
(b) opposite sides are 3 inches and 4 inches. Opposite angles are 45° and 135°
(c) yes, all side lengths can be determined, see (b)
Step-by-step explanation:
Opposite sides of a parallelogram are the same length, so if one side is 3 inches, so is the opposite side. Similarly, if one side is 4 inches, so is the opposite side. If sides have different lengths, they must be adjacent sides. The given numbers tell us the lengths of all of the sides.
The 4 inch sides are adjacent to the 3 inch sides. Thus the angle between a 4 inch side and a 3 inch side must be 45°. Opposite angles are congruent, and adjacent angles are supplementary, so specifying one angle specifies them all.
Only one parallelogram can be formed with these sides and angles. (The acute angle can be at the left end or the right end of the long side. This gives rise to two possible congruent orientations of the parallelogram. Because these are congruent, we claim only one parallelogram is possible. Each is a reflection of the other.)
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Answer:
x = 11
Step-by-step explanation:
In ΔSTU ,
m∠S = (11x+3)° ; m∠T = (2x+16)° ; m∠U = (x+7)°
According to angle sum property of a triangle , sum of all the interior angles of the triangle is 180°.
So,
Step-by-step explanation:
If X is a finite Hausdorff space then every two points of X can be separated by open neighborhoods. Say the points of X are . So there are disjoint open neighborhoods
and
, of
and
respectively (that's the definition of Hausdorff space). There are also open disjoint neighborhoods
and
of
and
respectively, and disjoint open neighborhoods
and
of
and
, and so on, all the way to disjoint open neighborhoods
, and
of
and
respectively. So
has every element of
in it, except for
. Since
is union of open sets, it is open, and so
, which is the singleton
, is closed. Therefore every singleton is closed.
Now, remember finite union of closed sets is closed, so is closed, and so its complemented, which is
is open. Therefore every singleton is also open.
That means any two points of belong to different connected components (since we can express X as the union of the open sets
, so that
is in a different connected component than
, and same could be done with any
), and so each point is in its own connected component. And so the space is totally disconnected.