Question

In the given figure △ABC ≅△DEC. Which of the following relations can be proven using CPCTC ?

Answer 1

Option B:

`\overline{A B}=\overline{D E}`

Solution:

In the given figure
`\triangle A B C \cong \triangle D E C`.

If two triangles are similar, then their corresponding sides and angles are equal.

By CPCTC, in
`\triangle A B C \ \text{and}\ \triangle D E C`,

`\overline{AB }=\overline{DE}` – – – – (1)

`\overline{B C}=\overline{EC}` – – – – (2)

`\overline{ CA}=\overline{CD}` – – – – (3)

`\angle ACB=\angle DCE` – – – – (4)

`\angle ABC=\angle DEC` – – – – (5)

`\angle BAC=\angle EDC` – – – – (6)

Option A:
`\overline{B C}=\overline{D C}`

By CPCTC proved in equation (2)
`\overline{B C}=\overline{EC}`.

Therefore
`\overline{B C}\\eq \overline{D C}`. Option A is false.

Option B:
`\overline{A B}=\overline{D E}`

By CPCTC proved in equation (1)
`\overline{AB }=\overline{DE}`.

Therefore Option B is true.

Option C:
`\angle A C B=\angle D E C`

By CPCTC proved in equation (4)
`\angle ACB=\angle DCE`.

Therefore
`\angle A C B\\eq \angle D E C`. Option C is false.

Option D:
`\angle A B C=\angle E D C`

By CPCTC proved in equation (5)
`\angle ABC=\angle DEC`.

Therefore
`\angle A B C\\eq \angle E D C`. Option D is false.

Hence Option B is the correct answer.

`\Rightarrow\overline{A B}=\overline{D E}`