Note, remember that when you name the triangles, the corresponding vertices should be in the same place.
For example, for the first pair of triangles, you know that the first triangle is named ΔGHI
The corresponding vertex for G is L, then the first letter on the name of the second triangle should be L.
Following the tick marks, and taking into consideration that corresponding sides should be equal, the corresponding vertex to H should be J, so J is the second letter on the name of the triangle.
The remaining vertex K is then the corresponding vertex to I and is, therefore, the third letter of the name of the triangle, then:
ΔLJK is the name of the second triangle on the first item of the exercise.
1) ΔGHI and ΔLJK
Two pairs of sides are congruent but this does not necessarily mean that they are congruent.
Both triangles will be congruent only if the angles between the congruent sides are also congruent.
If the congruent angle is one of the non-included angles, then the triangles may not be congruent.
So ΔGHI and ΔLJK are not nevesarly congruent
2) ΔUVW
Side WU and side YZ have one tick mark which means that they are congruent.
Side VW and side XZ have two tick marks which indicate that they are congruent.
The angles ∠UWV and ∠YZX are congruent.
For both triangles to be considered congruent, you have to name the second triangle so that the equal sides are congruent.
ΔUVW
Vertices U and Y should be in the same place so that sides WU and YZ are corresponding, so Y must be the first letter in the name of the triangle.
Vertices V and X should be in the same place so that sides VW and XZ are corresponding, so X should be the second letter of the name of the triangle.
Vertices W and Z must be in the same place so that both angles are corresponding.
The name of the second triangle is then ΔYXZ
Since the pairs of corresponding sides and the angle between them are congruent, the triangles can be considered congruent by Side-Angle-Side (SAS)
3) ΔABC
Angles ∠CAB and ∠DEF have the same mark, so they can be considered congruent.
Angles ∠ABC and ∠EDF have the same mark, which indicates that they can be considered congruent.
Sides AB and ED have one tick mark, which indicates that they are congruent.
For ∠CAB and ∠DEF to be considered corresponding, vertices A and E should be in the same place, so E is the first letter of the name of the second triangle.
For ∠ABC and ∠EDF to be considered corresponding, vertices B and D should be in the same place, so D is the second letter of the name of the second triangle.
Finally, for vertices C and F to be considered corresponding, the letter F should be the last letter in the name of the second triangle.
The name of the second triangle should be ΔEDF
Since both pairs of corresponding angles and the sides between them are congruent, the triangles can be considered congruent by Angle-Side-Angle (ASA)