Question

1. aas
2. hl
3. sss
4. sas

Explanation:

Step1: Identify AAS congruent triangles

For figure 31: $\angle C = \angle V$, $\angle CAB = \angle VBA$, $\overline{AB} = \overline{BA}$ (common side). So $\triangle ABC \cong \triangle BAV$ by AAS.

Step2: Identify HL congruent triangles

For figure 32: $\angle EFD = \angle EFV = 90^\circ$, $\overline{EF} = \overline{EF}$ (common leg), $\overline{ED} = \overline{EV}$ (hypotenuse). So $\triangle EFD \cong \triangle EFV$ by HL.

Step3: Identify SSS congruent triangles

For figure 33: $\overline{XI} = \overline{JI}$, $\overline{XK} = \overline{JK}$, $\overline{IK} = \overline{IK}$ (common side). So $\triangle XIK \cong \triangle JIK$ by SSS.

Step4: Identify SAS congruent triangles

For figure 34: $\overline{SR} = \overline{QW}$, $\angle SRQ = \angle WQR$, $\overline{RQ} = \overline{QR}$ (common side). So $\triangle SRQ \cong \triangle WQR$ by SAS.

Answer:

1. $\triangle ABC \cong \triangle BAV$
2. $\triangle EFD \cong \triangle EFV$
3. $\triangle XIK \cong \triangle JIK$
4. $\triangle SRQ \cong \triangle WQR$