Two triangles are congruent when they have identical sides and angles. Meaning that the three sides of one are equal to the sides of the other, and the three angles of one are equal to the angles of the other.
the symbol || and | in the figures indicate that the sides of that figure are equal.
The postulates are:
SSS= side side side
The three sides of one triangle are congruent to the three sides of the other one.
SAS= side angle side
two sides and the included angle are equal in both triangles.
ASA= angle side angle
Two angles and the included side of the triangle are equal in both triangles.
AAS= angle angle side
Two angles and the non included side (meaning that the side isn't between the two angles) are of equal lenght in both triangles.
HP= hypotenuse postulate
The hypotenuse and one of the sides of the triangle are of equal length.
Triangles NAM and JOB
Side NA = side OB
Side AM = side JO
Judging by the graphic, Side NM = side JB
∠NAM = ∠ JOB
For this triangle pair, the postulates that fit are:
SSS, SAS since all the sides are of equal length and at least one of the angles in both triangles are equal.
Triangles EBX and WXB
Side EX = side XW
Since they share it, side XB is the same lenght for both triangles.
There is no information abouth the length of EB and BW and there is no information about the anlges so you canot conclude these are congruent.
These triangles are not congruent.
