The two column proof is presented as follows;
Statement [tex]{}[/tex] Reasons
1. [tex]\overline{PQ}[/tex] ≅ [tex]\overline{QR}[/tex] [tex]{}[/tex] 1. Given
2. [tex]\overline{SQ}[/tex] bisects ∠PQR 2. Given
3. ∠PQS ≅ ∠RQS [tex]{}[/tex] 3. Definition of angle bisector
4. [tex]\overline{QS}[/tex] ≅ [tex]\overline{QS}[/tex] [tex]{}[/tex] 4. Reflexive property of congruency
5. ΔPQS ≅ ΔRQS [tex]{}[/tex] 5. SAS rule of congruency
6. ∠P ≅ ∠R [tex]{}[/tex] 6. CPCTC
Reasons:
3. An angle bisector is defined as a line that divides an angle in two.
4. Reflexive property is the property that a side is congruent to itself.
5. SAS: Side-Angle-Side rule of congruency states that, when two sides an
an included angle are congruent to two sides and an included angle in
another triangle, the two triangles are congruent.
6. CPCTC; Congruent Parts of Congruent Triangles are Congruent
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