How do I use properties of congruence to find unknown values?

In orde to find properties with an unknown values and notice if the triangles are congruentt all corresponding sides and interior angles of  the triangles need to have the same shape or size.

How do I use triangle sum properties to find unknown values?

The first step in order to find the unknown value of the triangle sum is to know that the sum of the measures of the interior angles of a triangle it has to equal  180. In order to know if this is equivalent to 180 you have to  use the facts that are given to you on the problem.When you are trying to find the unknown number you have to use the Triangle Angle Sum Theorem to solve for it which it is 

 after you have put the equation you need to substitude into the equation and if it is correct it has to equal 180.

How do I write linear equations passing through a given point?

 To find the equation of a line you need to know either two points or one point and the slope. If they are giving you two points, the first step is to find the slope from the two given points. So first you have to know  the slope formula which is Y= mx+b. After you have put the formula you have to put in the slope for m on either of the given points for ( x₁, y₁ ). The next step is convert it into a standard format. After you have done this steps, then you have to eliminate the denominator and you have to rearrange the terms of the equation. The next step to finish is just to change the sings and you are done :D