The proof to show that △PQO ≅ △RSO has been outlined by the 7 seven statement proof below.
The image of the triangles is missing and so i have attached it. The step by step statement proof to show that △PQO ≅ △RSO is as follows;
Statement 1; ∠P≅∠R
Reason 1; Given
Statement 2; O is midpoint of PR and QS
Reason 2; Given
Statement 3; PO ≅OR ;QO ≅OS
Reason 3; Definition of midpoint of a line
Statement 4; PQ ≅ RS
Reason 4; Given
Statement 5; ∠POQ ≅ ∠ROS
Reason 5; The angles are equal according to vertical angles theorem.
Statement 6; ∠Q ≅ ∠S
Reason 6; Angles are equal according to third angles theorem.
Statement 7; △PQO ≅ △RSO
Reason 7; Definition of congruent triangles.
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