2)

3)

4) yes - HA

5) yes - HL

6) yes - HL

7) angles Q and S are right angles , angle 1 = angle 2 - Given

Triangles PQR and RSP are right triangles - definition of right triangle

PR = PR - identity

Triangles PQR and RSP are congruent - HA

8) AC _|_ BE , CE _|_ AD , angle BAE = angle DEA - Given

angles ABE and EDA are right angles - perpendicular lines form right angles

angles ABE and EDA are congruent - all right angles are congruent

angles BFA and DFE are congruent - vertical angles congruent

angle BAF and DEF are congruent - if two angles in a triangle are congruent, then the third is congruent

angle FAE + angle BAF = angle BAE and angle FEA + angle DEF = angle DEA - angle addition

angle FAE = angle BAE - angle BAF and angle FEA = angle DEA - angle DEF - subtraction

angle FAE = angle BAE - angle BAF and angle FEA = angle BAE - angle DEF - substitution

angle FAE = angle FEA - substitution

AE = AE - identity

triangle BEA = triangle DAE - HA

BE = AD - CPCTC

9) BA = ED and AC = DF - given

triangle BAC = triangle EDF - LL

angle C = angle F - CPCTC