1. In an isosceles triangle PQR, with PQ = PR, the bisectors of
Q and R intersect each other at O. Join P to 0. Show that :
(i) OQ = OR
(ii) OP bisects 2 P
Answers
Answer:
Explanation:
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Given : an isosceles triangle PQR where PQ=PR
the bisectors of angle Q and R meet at O.
To find : Show that OQ = OR and
OPI is the bisector of angle P.
Solution:
isosceles triangle PQR
PQ = PR
=> ∠Q = ∠R ( angles opposite to equal sides are equal )
QI and RI are bisector of angle Q & angle R
=> ∠RQO = ∠Q/2
∠QRO = ∠R/2
∠Q = ∠R => ∠Q/2 = ∠R/2
=> ∠RQO= ∠QRO
=> OR = QR ( Sides opposites to equal angles are equal )
∠PQO = ∠Q/2
∠PRO = ∠R/2
=> ∠PQO = ∠PRO
in ΔPQO and ΔPRO
PQ = PR ( given )
∠PQI = ∠PRI
OQ = OR (shown above )
=> ΔPQO ≅ ΔPRO (SAS)
=> ∠QPO= ∠RPO
=> OP is bisector of ∠P
Shown that OQ = OR and OP is bisector of ∠P
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