Option A: establishes that the diagonals intersect at right angles, which is a property of a rhombus, but not sufficient.<span> Conclusion of "no" is incorrect.
Option B: </span>establishes that the diagonals intersect at right angles, which is a property of a rhombus, but not sufficient.
<span>Option C: establishes that the diagonals bisect each other, which is a property of a rhombus, but not sufficient.
Option D: </span>establishes that the diagonals intersect at right angles, which is a property of a rhombus, AND diagonals bisect each other. Together, the two properties are sufficient to establish that the figure is a rhombus.
<span>
Another sufficient condition to establish a rhombus is that the four sides are congruent, as follows:
If A(2, −1), B(5, −5), C(10, −5), and D(7, −1) are the vertices of a rhombus IN ORDER, then AB, BC, CD, DA are the sides.
It is sufficient to prove that the four sides are congruent to conclude that ABCD is a rhombus. (can be established by joining diagonals and proving congruence of triangles by SSS).
mAB=sqrt((5-2)^2+(-5-(-1))^2)=sqrt(3^2+4^2)=5
similarly,
mBC=sqrt(5^2+0)=5
mCD=sqrt(3^2+4^2)=5
mDA=sqrt(5^2+0)=5
Since all four sides are congruent, the figure is a rhombus.
</span>
B because none of the angles as acute
Answer:
5![\sqrt{6}](https://tex.z-dn.net/?f=%5Csqrt%7B6%7D)
Step-by-step explanation:
Using the rule of radicals
×
⇔ ![\sqrt{ab}](https://tex.z-dn.net/?f=%5Csqrt%7Bab%7D)
Given
![\sqrt{150}](https://tex.z-dn.net/?f=%5Csqrt%7B150%7D)
= ![\sqrt{25(6)}](https://tex.z-dn.net/?f=%5Csqrt%7B25%286%29%7D)
=
× ![\sqrt{6}](https://tex.z-dn.net/?f=%5Csqrt%7B6%7D)
= 5![\sqrt{6}](https://tex.z-dn.net/?f=%5Csqrt%7B6%7D)
Answer:
Step-by-step explanation:
the slope is 1/1
Answer:
The third option: x= ![\frac{8}{3} \pi](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B3%7D%20%5Cpi)
Step-by-step explanation:
Arc length formula=![\frac{Central Angle}{360} * 2\pi r](https://tex.z-dn.net/?f=%5Cfrac%7BCentral%20Angle%7D%7B360%7D%20%2A%202%5Cpi%20r)
Arc length = ![\frac{120}{360} *2\pi (4)](https://tex.z-dn.net/?f=%5Cfrac%7B120%7D%7B360%7D%20%2A2%5Cpi%20%284%29)
=![\frac{8}{3}\pi](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B3%7D%5Cpi)