PQR IS A ISOSCELES TRIANGLE IN WHICH PQ=PR, PS BISECTS EXTERIOR ANGLE MPR AND RS // PQ SHOW THAT ANGLE SPR= ANGLE QPR AND PQRS IS A PARRELOGRAM
Answers
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
Step-by-step explanation:
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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