Question

In triangle PQR PQ = PR, QP is produced to T so that PQ=PT. find measure angle TRQ.​

Answer 1

Answer:

Given: △PQR is an isosceles triangle with PQ=PR

Proof: PT bisects exterior angle ∠SPR and therefore ∠SPT=∠TPR=x

o

∴ ∠Q=∠R (Property of an isosceles triangle)

also we know that in any triangle,

exterior angle= sum of the interior opposite angles.

∴ In △PQR, Exterior angle ∠SPR=∠PQR+∠PRQ

2x

o

=∠Q+∠R

=∠Q+∠Q

2x

o

=2∠Q

x

o

=∠Q

To prove: PT∥QR

Lines PT and QR are cut by the transversal SQ. We have ∠SPT=x

o

Hence, ∠SPT and ∠PQR are corresponding angles: PT∥QR