Segment RT bisects ∠QRS in ΔQRS and therefore, the angles ∠1 and ∠2
formed are equal.
The valid reason for the statement ∠1 ≅ ∠2 is; A. Definition of Angle Bisector.
Reasons:
The information on the triangle ΔQRS are;
The angle bisector of ∠QRS = RT
Therefore;
∠QRT = ∠1, ∠SRT = ∠2 Given in the diagram
∠QRS = ∠QRT + ∠SRT by angle addition property
∠QRT ≅ ∠SRT by definition of angle bisector
∠1 ≅ ∠2 by definition of ∠QRT and ∠SRT
By substituting ∠QRT with ∠1 and ∠SRT with ∠2, we have;
∠1 ≅ ∠2 by definition of angle bisector
The valid reason for the statement is therefore; A. Definition of angle
bisector.
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