Determine whether the congruence is true or false. 11equiv 15 mod 4

To determine: The smallest nonnegative integer x that satisfies the given system of congruences.
${\displaystyle x\equiv 3\pm od\left\{1917\right\}}$
${\displaystyle x\equiv 75\pm od\left\{385\right\}}$

To find: congruent criteria used to prove that the triangles are congruent.
Given information:
${\displaystyle \mathrm{\angle }ABC\stackrel{\sim }{=}\mathrm{\angle }ACB,\overline{AE}\perp \overline{EC}\text{and}\overline{AD}\perp \overline{DB}}$

State the third congruence required to prove the congruence of triangles using the indicated postulate.

a)${\displaystyle \overline{ZY}\stackrel{\sim }{=}\overline{JL}}$
b)${\displaystyle \mathrm{\angle }X\stackrel{\sim }{=}\mathrm{\angle }K}$
c)${\displaystyle \overline{KL}\stackrel{\sim }{=}\overline{XZ}}$
d)${\displaystyle \mathrm{\angle }Y\stackrel{\sim }{=}\mathrm{\angle }L}$

To prove: If the convex quadrilateral ABCD has opposite sides congruent, then the opposide sides are parallel.
Given:
The given figure is,

Figure-(1)

How many sides does a hexagon have?

Consider the system of linear congruences below:
${\displaystyle x\equiv 2\left(\text{mod}5\right)}$
${\displaystyle 2x\equiv 22\left(\text{mod}8\right)}$
${\displaystyle 3x\equiv 12\left(\text{mod}21\right)}$
(i)Determine two different systems of linear congruences for which the Chinese Remainder Theorem can be used and which will give at least two of these solutions.

For the triangles shown, we can express their congruence with the statement ${\displaystyle \mathrm{△}ABC\stackrel{\sim }{=}\mathrm{△}FED}$. By reordering the vertices, express this congruence with a different statement.