Based on the given information, what can you conclude, and why?
Given: m angle P=m angle T , PR = TR
R
P
(1 point)
A. triangle QRP cong triangle TRS by SAS.
B.triangle QRP cong triangle SRT by SSS.
C.triangle QRP cong triangle SRT by ASA
D. triangle ORP cong triangle STR by ASA
It is not possible to conclude any of the given statements based on the information provided. The given information only states that angle P is congruent to angle T and that PR is equal to TR. It does not provide enough information to determine any congruence statements between triangles QRP and TRS or SRT.
Based solely on the given information, we can conclude that triangle QRP is congruent to triangle TRS by the Side-Angle-Side (SAS) congruence criterion.
This is because we are given that angle P is equal to angle T, and PR is equal to TR. With these two pieces of information, we have matching corresponding parts: PQ = TS, angle P = angle T, and PR = TR. These matching congruent parts satisfy the SAS criterion, leading to the conclusion that triangle QRP is congruent to triangle TRS.
Therefore, the correct answer is A. triangle QRP is congruent to triangle TRS by SAS.
Based on the given information, we can conclude that triangle QRP is congruent to triangle SRT. To understand why, we need to look at the congruence postulates.
One of the congruence postulates is the Side-Angle-Side (SAS) congruence postulate. This postulate states that if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the triangles are congruent.
In the given information:
- Angle P is congruent to angle T.
- PR is congruent to TR.
According to the SAS postulate, this means that triangle QRP is congruent to triangle SRT.
Therefore, the correct answer is A. Triangle QRP is congruent to triangle SRT by SAS.