Question

given: ∠p≅∠t, r is the mid - point of (overline{qs}) prove: △pqr≅△tsr statement reason 1. ∠p≅∠t 1. 2. r is the mid - point of (overline{qs}) 2. 3. ∠qrp≅∠srt 3. 4. (overline{qr}congoverline{rs}) 4. 5. △pqr≅△tsr 5. given sss sas aas asa hl definition of midpoint definition of angle bisector reflexive property corresponding angles alternate interior angles vertical angles

Explanation:

Step1: State given angle

Given

Step2: State given mid - point

Given

Step3: Identify vertical angles

Vertical angles are congruent

Step4: Use mid - point definition

Definition of Midpoint

Step5: Prove triangles congruent

AAS (Two angles and a non - included side are congruent)

Answer:

1. Given
2. Given
3. Vertical Angles
4. Definition of Midpoint
5. AAS