Question

6. In the given figure, AB = AC; ZA = 50° and angle ACD = 15°.
Show that BC = CD.​

Answer 1

Answer:

hey here is your proof

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so here we go

Step-by-step explanation:

now as here ab=ac

because of isoceles triangle theorem,

angle acb=angle abc

so let angle abc=acb=x

now as angle a=50 here

so apply angle sum property on triangle abc

we get angle a+x+x=180

ie 2x=130

so x=65

so angle acb=abc=65 (1)

now again also angle dac=angle bac=50

since (b-d-a)

so as here acd=15

apply angle sum property on triangle adc

you get

angle adc+50+15=180

so thus angle adc=115

now angle acd+angle dcb=angle acb

so angle dcb+15=65 (from 1)

so hence angle dcb=50 (2)

now here also angle abc=dbc=65 (a-d-b) (3)

so apply angle sum property on triangle dcb

you get angle bdc+dcb+cbd=180

ie angle bdc+65+50=180 (from 3 and 2)

ie angle bdc=180-115

so angle bdc=65 (4)

so in same triangle as base angles ie

angle bdc=dbc=65 (from 3 and 4)

side cd=bc by converse of isoceles triangle theorem.

hence proved

Answer 2

the ans which that person gave it perfect u can note down that ans