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IRISSAK [1]
3 years ago
15

Based on the given information, what can you conclude and why

Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
8 0
Notice the point R
is a vertex between two "vertical angles" \measuredangle SRT\ and\ \measuredangle QRP

those two folks are also the same
so now, we have the left triangle has angle P equals to angle T on the other triangle
we also have the side on the left triangle of PR equals the side of TR on the other triangle, and those two verticals angles are equal to each other

does ASA ring a bell?
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Option B:

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

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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}

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

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Therefore Option B is true.

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

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

Hence Option B is the correct answer.

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

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