Question

In the figure,if AC is the bisector of angle A. Show that
(i) AB>BD
(ii) AC>CD​

Answer 1

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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