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

In the given figure △ABC ≅△DEC. Which of the following relations can be proven using-example-1
User Tha Leang
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1 Answer

1 vote

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}

User AaronMK
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