PQRS is a rectangle and T is the mid-point of PQ then prove \$\triangle SPT \cong \triangle RQT\$.

\$ED ∥ AC\$ and B is the mid-point of ED. Prove \$\triangle EAB \cong \triangle DCB\$.

\$AG ∥ BE\$, \$BE \bot AC\$ and B is the mid-point of AC. Prove \$\triangle ABD \cong \CBD\$.

MNOP is a square, Q is the mid-point of MO and NP and \$NQ \bot MO\$. Prove \$\triangle NQM \cong \triangle NQO\$.

UT = QR and V is the mid-point of UR and TQ. Prove \$\triangle TVU \cong \triangle QVR\$.