Based only on the information given in the diagram, the congruence theorems or postulates that could be given as reasons why ΔCDE ≅ ΔOPQ are:
B. AAS
D. HL
F. LA
In Mathematics and Euclidean Geometry, AAS is an abbreviation for Angle-Angle-Side and it states that when two (2) angles and the non-included side (adjacent to only one of the angles) in two triangles are all equal, then the triangles are said to be congruent.
Based on the Angle-Angle similarity Postulate, triangle CDE is congruent to triangle OPQ;
m∠C ≅ m∠O = 90°
m∠E ≅ m∠Q
DE ≅ PQ
By applying the hypotenuse leg (HL) theorem across right-angled triangle CDE and OPQ, we have the following;
DC ≅ OP (Leg of the triangle)
DE ≅ PQ (Hypotenuse)
By applying the leg and acute angle (LA) theorem across right-angled triangle CDE and OPQ, we have the following;
DE ≅ PO
m∠E ≅ m∠Q