In the figure below, APQR is a reflection of ATSA.
Two students describe the given triangles as shown:
Student I: Because reflections preserve side lengths, OR a SR, PO TS, and PR TR.SO APORATSR by SSS.
Student II: Because reflections preserve both side lengths and angle measures, ZROP ZRST, OR SR. and PO = TS. SO APOA - ATSR by SAS.
Who has proven APOR - ATSR correctly?
only studenti
only student II
o
both student I and student II
o
neither student I nor student II

Congruent triangle-If the sides of two triangle measure same lengths and the angle have same measures then the two triangle are said to be congruent.

Given-

Statement of student 1-Because reflections preserve side lengths,

[tex]QR \cong SR[/tex],

[tex]PQ \cong TS[/tex],

[tex]PR \cong TR.[/tex] so,

[tex]\bigtriangleup PQR \cong \bigtriangleup TSR[/tex]

In all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangle are said to be congruent by the side side side (SSS) rule. Hence, the above statement is correct.

Statement of student 2- Because reflections preserve both side lengths and angle measures,

[tex]\angle RQP \cong \angle RST[/tex]

[tex]QR \cong SR[/tex]

[tex]PQ \cong TS[/tex]

[tex]\bigtriangleup PQR \cong \bigtriangleup TSR[/tex]

In any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangle are said to be congruent by the side angle side (SAS) rule. Hence the above statement is correct.

Hence, with the properties of congruent triangle we conclude that the statement of both student I and student II are correct.

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