Question

In the figure, RS = QT and QS = RT. Prove the PQ = PR. R​

Answer 1

Answer:

Let QS RT meet at U

Consider △RUS and △QUT

RS=QT

QS=RT

∠RUS=∠QUT

⟹△RUS,△QUT are congruent

Consider △PRT and △PQS

∠PRT=∠PQS

∠RTP=∠QSP

RT=SQ

⟹△PRT,△PQS are congruent

⟹PQ=PR

Hence proved

Answer 2

Answer:

${ \large{ \underline { \sf{Solution-}}}}$

Let Us Consider, RUS and QUT as Two Triangles.

From △QUT and △RUS:-

According to question, RS = QT and QS = RT

${ \sf{So, { \angle{u}} = { \angle{u}} \: \: \: (common \: angle)}}$

${ \therefore{ \sf{{ \angle{RUS }} = { \angle{QUT}}}}}$

They Both are Congruent.

Now,

From △PRT and △PQS:-

${ \sf{{ \angle{T } = { \angle{S}} \: \:So, ∠RTP=∠QSP }}}$

${ \sf{Also, \angle{ R} = \angle{Q} \: \: \: So, ∠PRT=∠PQS}}$

From Angles,

RT = QS , Both triangles are also congruent.

${ \therefore{ \underline{ \sf{PQ = PR}}}}\:$

Hence Proved