In the figure,if AC is the bisector of angle A. Show that
(i) AB>BD
(ii) AC>CD
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Answer:
Step-by-step explanation:
In △ABC,
⇒ AB=AC [ Given ]
⇒ ∠ABC=∠ACB [ Base angles of equal sides are also equal. ]
⇒ ∠ABC=75
o
∴ ∠ACB=75
o
⇒ ∠ABC+∠ACB+∠BAC=180
o
⇒ 75
o
+75
o
+x=180
o
⇒ 150
o
+x=180
o
⇒ x=30
o
.
It is given that, AC bisects ∠A
∴ ∠BAC=∠CAD
∴ ∠CAD=30
o
In △ACD,
⇒ AD=CD [ Given ]
⇒ ∠CAD=∠ACD [ Base angles of equal sides are also equal. ]
∴ ∠ACD=30
o
⇒ ∠CAD+∠ACD+∠CDA=180
o
⇒ 30
o
+30
o
+y=180
o
⇒ 60
o
+y=180
o
⇒ y=120
o
∴ The value of x and y are 30
o
and 120
o
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