It helps to list the congruent parts in the correct order. If an angle is included, write it in the second line.
See solution.
Practice makes perfect
When we want to prove a triangle congruence, we need to identify the corresponding congruent parts between both triangles. Depending on these parts we will use a particular method.
Congruence Postulates
Side-Side-Side
Side-Angle-Side
Angle-Side-Angle
Angle-Angle-Side
In any case, we need three pairs of corresponding congruent parts. To determine which postulate to use, it helps to list the congruent parts in the correct order. We have four cases:
When we have three pairs of congruent sides, we list each one below the other. Here the order is not relevant.
When we have two pairs of congruent sides and the pair of congruent angles are the included ones, we list them in such a way that the angles are written in the second line.
When we have two pairs of congruent angles and the pair of congruent sides are the included ones, we list them in such a way that the sides are written in the second line.
When we have two pairs of congruent angles and the pair of congruent sides are the non-included ones, we list them in such a way that the sides are written in the third line.
As we can see from each diagram, identifying and listing the congruent parts in the correct order automatically will tell us which postulate to use.
