Prove the congruence \overline{UQ}\cong\overline{VQ}

snowlovelydayM

snowlovelydayM

Answered question

2021-07-17

To prove: UQ=VQ
Given information:
SU=SV,1=2

Answer & Explanation

davonliefI

davonliefI

Skilled2021-07-18Added 79 answers

Proof:
image

Consider UQS,VQS
SU=SV (Given)
1=2 (Given)
QS=SQ (As per reflexive property of congruence, if l is a line segment then l=l)
So,
UQS=VQS
(In accordance with the SAS congruence criteria, two triangles are deemed to be congruent if their two sides and any included angles are parallel to each other.)
Therefore,
UQ=VQ (corresponding sides of congruent triangles are congruent)

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