Explanation:
In Triangle ICU,
Angle 2 = 180° - Angle 1 (Angles on a straight line)
CR = CU - RU
In Triangle ISR,
Angle 3 = 180° - Angle 4(Angles on a straight line)
SU = RS - RU
Angle 1 = Angle 4
Therefore, Angle 2 is equal to Angle 3
CU = RS
Therefore, CR is equal to SU
Triangle ICR and Triangle ISU
IC = IS
Angle 2 = Angle 3
CR = SU
Therefore, Triangle ICR and Triangle ISU are congruent (SAS congruency).
As the two triangles are congruent, Angle CIR = Angle SIU