Which of the following is the correct equation used to solve for the measure of each angle? OA. mangle A−mangle B−mangle C=180∘ O B. mangle A+mangle B

These two triangles are similar by AA similarity. The ratio of corresponding altitudes is proportional to the ratio of corresponding sides. Find the value of x.
Given,
Two triangles are similar by angle-angle similarity,

To Complete:the statement WZ=? and RS=? in the figure shown.
Given:
Figure is shown below.

RW=15, ZR=10 and ZS=8

Are the two triangles similar? If so, by what similarity shortcut?

SSS
SAS
AA
Not Similar

To prove:The congruency of ${\displaystyle \overrightarrow{MH}\stackrel{\sim }{=}\overrightarrow{JO}}$.
Given information:
The following information has been given GJKM is a rhombus
${\displaystyle \mathrm{\angle }JOG=\mathrm{\angle }MHG={90}^{\circ }}$

Prove that if $a,b,c\in \mathbb{R}$ are all distinct, then $a+b+c=0$ if and only if $(a,a^3),(b,b^3),(c,c^3)$ are collinear.

Gauss-divergence theorem for volume integral of a gradient field
I need to make sure that the derivation in the book I am using is mathematically correct. The problem is about finding the volume integral of the gradient field. The author directly uses the Gauss-divergence theorem to relate the volume integral of gradient of a scalar to the surface integral of the flux through the surface surrounding this volume, i.e.
${\int }_{CV}^{}\mathrm{\nabla }\varphi dV={\int }_{\delta CV}^{}\varphi d\mathbf{S}$

Theorems that we can prove only by contradiction