Question

10. ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC
and ADC.
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Answer 1

Step-by-step explanation:

According to the question, In ΔABC and ΔCBD, We have AB = BC AD = CD BD = BD [Common side] ΔABC ≅ ΔCBD [By SSS congruence rule] ⇒ ∠1 = ∠2 [CPCT] And ∠3 = ∠4 Hence, BD bisects both ∠ABC and ∠ADC.

Answer 2

ANSWER

In △ABD and △CBD,

AD=CD [ given ]

BD=BD [ Common ]

AB=BC [ given ]

Hence, △ABD≅△CBD [ SSS ]

∠ABD=∠1

∠CBD=∠2

∠1=∠2 [ CPCT ]

Also ,

∠3=∠4 [ CPCT ]

Hence ,

BD bisects both the angles ABC and ADE