Answer:
1. SSS
2. SAS
3. SAS
4. SSS
5. SAS
6. SAS
Step-by-step explanation:
1) Side FY ≅ Side CW  Given
Side FP ≅ Side CM     Given
Side YP ≅ Side MW    Given
∴ΔMCW ≅ ΔFPY by the Side-Side-Side (SSS) rule of congruency
2) ∠CBD ≅ ∠BCA given that both are alternate interior angles
Side EB ≅ Side EC and Side DB ≅ Side CA Given
ΔBED ≅ ΔAEC by Side-Angle-Side (SAS) rule of congruency
3. ∠SVU ≅ ∠SVT   Given
Side SV ≅ Side SV  by reflexive property
Side VT ≅ Side VU   Given
∴ ΔVSU ≅ ΔVST by Side-Angle-Side (SAS) rule of congruency
4. Side MN ≅ Side QP  Given
Side MQ ≅ Side NP     Given
Side NQ ≅ Side NQ    by reflexive property
∴ΔQNM ≅ ΔQNP by the Side-Side-Side (SSS) rule of congruency
5. Indirect proof
Side GL ≅ Side HL  Given
Side GJ ≅ Side HK     Given
∠JLG ≅ ∠HLK    vertically opposite angles
By sine rule
GJ/sin(∠JLG) = GL/n(∠GJL)
Similarly
HK/sin(∠HLK) = HL/n(∠HKL)
∴ ∠GJL ≅ ∠HKL
∴ ∠LGJ ≅ ∠LHK third angle of two triangles given the other two angles are congruent
∴ΔQNM ≅ ΔQNP by the Side-Angle-Side (SAS) rule of congruency
6. ∠XZY ≅ ∠XZW   Supplementary ∠s with ∠XZY = 90°
Side XZ ≅ Side XZ  by reflexive property
Side ZW ≅ Side ZY   Given
∴ ΔXYZ ≅ ΔXWZ by Side-Angle-Side (SAS) rule of congruency.