Question

AOC and BOD are diameters of a circle, centre O. Prove that triangle ABD and triangle DCA are congruent by RHS. B D ​

Answer 1

Given:

`\text{AOC}` and
`\text{BOD}` are diameters of a circle and has center
`\text{O}`.

To Find:

`\Delta\text{ABD}` and
`\Delta\text{DCA}` are congruent by
`\text{RHS}`.

Solution:

It is given that
`\text{AOC}` and
`\text{BOD}` are diameters of a circle.

`\rightarrow \text{BD} = \text{CA}` [diameters of the circle]

`\rightarrow \angle\text{BAD} = \angle\text{CDA}` [angles in semicircle is 90°]

`\rightarrow \text{AD} = \text{AD}` [common in both the triangles]

`\rightarrow \Delta\text{ABD} \cong \Delta\text{DCA}` [using RHS congruence criteria]

Hence, proved
`\Delta\bold{ABD} \cong \Delta\bold{DCA}` by
`\bold{RHS}` congruency criteria.