Question

in the figure ab is equal to CD prove that x is equal to y​

Answer 1

Answer:

yes

Step-by-step explanation:

given that ab is equal to cd ,

we have prove that x is equal to y

According to eculid axioms opposite side are equal

Answer 2

Answer:

SAS CRITERION of CONGRUENCY will be applicable

Step-by-step explanation:

Given that

AB = CD

we know that equal chords subtends equal angle on centre.

Thus

$\angle \: AOB \: = \angle \: COD \: ...eq1\:$

Now in triangle AOC and BOD

AO=BO (Radius of circle)

OC=OD (Radius of circle)

$\angle \: AOC = \angle \: AOB + \angle \: BOC \: ...eq2 \\ \\ \angle \: BOD = \angle \: COD + \angle \: BOC \: ...eq3$

from eq1 we know that angle AOB = angle COD

and an equal angle BOC is added into both equal angles.

(when equals added to equals resultant will be equal)

Thus

$\angle \: AOC= \angle \: BOD$

Thus by SAS CRITERION of CONGRUENCY

$\triangle \: AOC \cong \: \triangle \: BOD$

Thus by CPCT

$\angle OAC = \angle OBD \\ \\ \angle x = \angle y$

Hence proved